Preparing for IBPS PO, SBI PO, RBI Assistant, LIC AAO, SSC CGL, RRB NTPC, or any other competitive exam? This comprehensive practice set contains 100 original Profit and Loss questions designed at a moderate difficulty level to match the latest banking exam pattern.

Each question includes a step-by-step solution, shortcut method, and exam tip to help you improve both accuracy and calculation speed. The questions progress from basic to moderate level, making this collection suitable for beginners as well as serious aspirants.

Practice these questions regularly to strengthen your concepts, master important Profit and Loss formulas, and boost your confidence for the Quantitative Aptitude section of competitive exams.

Profit and Loss Formulas for Competitive Exams

📘 Important Profit and Loss Formulas

Before solving Profit and Loss questions, it’s important to understand the basic formulas. These formulas are frequently used in banking, SSC, railway, insurance, and other competitive examinations.

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1. Profit

Profit = Selling Price (SP) − Cost Price (CP)

Use this formula when the selling price is greater than the cost price.

2. Loss

Loss = Cost Price (CP) − Selling Price (SP)

Use this formula when the selling price is less than the cost price.

3. Profit Percentage

Profit % = (Profit ÷ Cost Price) × 100

Remember: Profit percentage is always calculated on the Cost Price.

4. Loss Percentage

Loss % = (Loss ÷ Cost Price) × 100

Loss percentage is also calculated on the Cost Price.

5. Selling Price

If Profit is given:

Selling Price = Cost Price + Profit

If Loss is given:

Selling Price = Cost Price − Loss

6. Selling Price Using Percentage

If Profit % is given:

SP = CP × (100 + Profit%) ÷ 100

If Loss % is given:

SP = CP × (100 − Loss%) ÷ 100

7. Cost Price

If Profit % is given:

CP = (SP × 100) ÷ (100 + Profit%)

If Loss % is given:

CP = (SP × 100) ÷ (100 − Loss%)

8. Marked Price

Marked Price (MP) = Selling Price × 100 ÷ (100 − Discount%)

This formula is useful when the Selling Price and Discount are known.

9. Discount

Discount = Marked Price − Selling Price

10. Discount Percentage

Discount % = (Discount ÷ Marked Price) × 100

11. Selling Price After Discount

SP = MP × (100 − Discount%) ÷ 100

12. Marked Price After Markup

MP = CP × (100 + Markup%) ÷ 100

13. Successive Discount

Net Discount = A + B − (A × B ÷ 100)

Example:

20% and 10%

Net Discount = 20 + 10 − 2 = 28%

14. Effective Cost Price

Effective Cost Price = Purchase Cost + Transportation + Labour + Packaging + Insurance + Repair + Other Expenses

Always include additional expenses while calculating profit or loss.

15. No Profit, No Loss

When:

Cost Price = Selling Price

then

Profit = 0 and Loss = 0

16. Profit on Selling Price

If Profit Percentage is calculated on the Selling Price:

Profit % = (Profit ÷ Selling Price) × 100

Read the question carefully to identify whether the percentage is based on the Cost Price or the Selling Price.

17. Loss on Selling Price

If Loss Percentage is calculated on the Selling Price:

Loss % = (Loss ÷ Selling Price) × 100

This type of question is less common but occasionally appears in competitive exams

18. Relationship Between Profit and Loss

• If Selling Price > Cost Price, there is Profit.
• If Selling Price < Cost Price, there is Loss.
• If Selling Price = Cost Price, there is No Profit, No Loss.

💡 Quick Revision Tips

• Profit and Loss percentages are generally calculated on the Cost Price, unless the question states otherwise.
• Never ignore transportation, packaging, labour, repair, or insurance charges. These increase the Effective Cost Price.
• Do not add successive discounts directly. Always use the successive discount formula.
• In percentage-based questions, assuming Cost Price = ₹100 often makes calculations much faster.
• Practice these formulas regularly to improve both speed and accuracy in competitive examinations.

📌 Question 1

📝 Question

A trader purchases an article at 20% below its marked price. He spends an additional ₹360 on transportation and packaging. He then marks the article 50% above his effective cost and allows two successive discounts of 10% and 20% on the marked price. If he finally earns a profit of ₹1,080, find the original purchase price of the article.

⚡ Shortcut Method

Let original purchase price = ₹x

Marked Price = x ÷ 0.80 = 1.25x

Effective CP = x + 360

Final SP

= (x + 360) × 1.50 × 0.90 × 0.80

= 1.08(x + 360)

Since profit = ₹1,080:

SP = x + 1,080

Therefore,

1.08(x + 360) = x + 1,080

1.08x + 388.8 = x + 1,080

0.08x = 691.2

x = ₹8,640

✅ Final Answer

₹8,640

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📌 Question 2

📝 Question

A merchant purchases 100 articles at the same cost price per article. He sells 30% of the articles at a profit of 20%, 40% of the articles at a profit of 10%, and the remaining articles at a selling price of ₹1,540 each. If his overall profit is 20%, find the cost price per article.

⚡ Shortcut Method

Let the cost price per article be ₹x.

There are 100 articles:

• 30 articles sold at 20% profit → SP = 30 × 1.20x = 36x
• 40 articles sold at 10% profit → SP = 40 × 1.10x = 44x
• Remaining 30 articles sold at ₹1,540 each → SP = 30 × 1,540 = ₹46,200

Overall profit = 20%, so total SP = 120% of total CP:

Total CP = 100x
Total SP = 120x

Therefore,

36x + 44x + 46,200 = 120x

80x + 46,200 = 120x

46,200 = 40x

x = ₹1,155

✅ Final Answer

₹1,155 per article

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📌 Question 3

📝 Question

A dishonest dealer buys goods at ₹100 per kg. When purchasing, he uses a faulty scale that shows 1,000 g when he actually takes 1,100 g for the same price. When selling, he marks his goods 20% above his nominal cost price and uses a false weight of 800 g instead of 1 kg. Find his overall actual profit percentage.

⚡ Shortcut Method

Let’s solve it carefully by taking 1 kg as the nominal unit.

⭐ Shortcut Method

At the time of purchase:

He pays ₹100 for a scale reading of 1,000 g, but actually receives 1,100 g.

So, actual cost of 1 kg:

₹100 × 1000/1100 = ₹90.91

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At the time of selling:

He marks the nominal cost price 20% above ₹100:

Selling price for a nominal 1 kg =

₹100 × 120% = ₹120

But he gives only 800 g while charging ₹120.

Therefore, actual selling price per 1 kg:

₹120 × 1000/800 = ₹150

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Actual Profit %

Profit = ₹150 − ₹90.91 = ₹59.09

Profit % = (59.09 / 90.91) × 100

= 65%

✅ Final Answer

65% Actual Profit

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📌 Question 4

📝 Question

A shopkeeper marks an article 60% above its cost price. He offers a discount of 20% and then an additional discount of x% on the reduced price. Even after both discounts, he earns a profit of 12%. Find x.

⚡ Shortcut Method

Assume CP = ₹100

MP = ₹160

After 20% discount:

160 × 0.80 = ₹128

Required SP for 12% profit = ₹112

Therefore,

128 × (100 − x)% = 112

(100 − x)% = 112/128

= 87.5%

x = 12.5%

✅ Final Answer

12.5%

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📌 Question 5

📝 Question

A trader buys two machines for a total of ₹1,20,000. He sells the first machine at a 20% profit and the second at a 10% loss. If the selling price of the first machine is ₹18,000 more than that of the second machine, find the cost price of each machine.

⚡ Shortcut Method

Let CP of first machine = ₹x

CP of second = ₹1,20,000 − x

Selling prices:

First = 1.20x

Second = 0.90(1,20,000 − x)

Difference = ₹18,000

1.20x − 0.90(1,20,000 − x) = 18,000

1.20x − 1,08,000 + 0.90x = 18,000

2.10x = 1,26,000

x = ₹60,000

Second CP = ₹60,000

✅ Final Answer

First Machine = ₹60,000
Second Machine = ₹60,000

📌 Question 6

📝 Question

A trader purchased 400 electric kettles at ₹1,500 each. He spent ₹30,000 on transportation and ₹10,000 on insurance. During transit, 20 kettles were damaged and sold at 40% of their effective cost price. The remaining 380 kettles were sold at a 25% profit on their effective cost price, with an online marketplace deducting a 4% commission on their selling price. Find the trader’s overall profit percentage.

⚡ Shortcut Method

Let’s calculate it carefully.

⭐ Shortcut Method

1. Total effective cost

Purchase cost:

400 × ₹1,500 = ₹6,00,000

Additional expenses:

₹30,000 + ₹10,000 = ₹40,000

Total effective cost:

₹6,00,000 + ₹40,000 = ₹6,40,000

So, effective cost per kettle:

₹6,40,000 ÷ 400 = ₹1,600

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2. Damaged 20 kettles

They are sold at 40% of effective cost:

SP per damaged kettle = 40% of ₹1,600 = ₹640

SP from 20 kettles:

20 × ₹640 = ₹12,800

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3. Remaining 380 kettles

They are sold at 25% profit on effective cost:

SP per kettle = 125% of ₹1,600 = ₹2,000

Gross SP:

380 × ₹2,000 = ₹7,60,000

Marketplace commission = 4% of ₹7,60,000:

= ₹30,400

Net SP:

₹7,60,000 − ₹30,400 = ₹7,29,600

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4. Total actual SP

= ₹12,800 + ₹7,29,600

= ₹7,42,400

Profit:

₹7,42,400 − ₹6,40,000 = ₹1,02,400

Therefore,

Profit % = (₹1,02,400 ÷ ₹6,40,000) × 100

= 16%

✅ Final Answer

16% Overall Profit

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📌 Question 7

📝 Question

A retailer marks an article 80% above its cost price. He offers a discount of 15%, followed by another discount of x%. Even after both discounts, he earns a 22.4% profit. Find the value of x.

⚡ Shortcut Method

Assume CP = ₹100

MP = ₹180

Required SP = 122.4% of ₹100

= ₹122.40

After 15% discount:

180 × 85%

= ₹153

Therefore,

153 × (100 − x)% = 122.40

(100 − x)% = 122.40 ÷ 153

= 80%

Therefore,

x = 20%

✅ Final Answer

20%

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📌 Question 8

📝 Question

A trader purchases two types of laptops. He buys 40 laptops of Type A at ₹30,000 each and 60 laptops of Type B at ₹20,000 each. He sells 25% of Type A laptops at a 20% profit and 50% of Type B laptops at a 12% loss. The remaining laptops of both types are sold at the same selling price per laptop. If the trader earns an overall profit of 15%, find the selling price of each remaining laptop.

⚡ Shortcut Method

Total CP

= (40 × 30,000) + (60 × 20,000)

= ₹24,00,000

Required total SP

= 24,00,000 × 115%

= ₹27,60,000

Type A sold at 20% profit:

= 10 × 30,000 × 120%

= ₹3,60,000

Type B sold at 12% loss:

= 30 × 20,000 × 88%

= ₹5,28,000

SP already received

= 3,60,000 + 5,28,000

= ₹8,88,000

Required SP from remaining 60 laptops

= 27,60,000 − 8,88,000

= ₹18,72,000

Selling price per remaining laptop

= 18,72,000 ÷ 60

= ₹31,200

✅ Final Answer

₹31,200 per laptop

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📌 Question 9

📝 Question

A dishonest wholesaler buys sugar at ₹48 per kg but uses a 900 g weight while purchasing. While selling, he uses an 800 g weight and charges his customers for 1 kg at ₹52. Find his actual profit percentage.

⚡ Shortcut Method

For ₹48, he actually receives 900 g.

Cost of 1 kg actually obtained

= 48 ÷ 0.9

= ₹53.33

While selling, he gives only 800 g for ₹52.

Actual SP per kg

= 52 ÷ 0.8

= ₹65

Profit %

= (65 − 53.33) ÷ 53.33 × 100

= 21.875%

✅ Final Answer

21.875% Profit

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📌 Question 10

📝 Question

A wholesaler purchases 600 office chairs at ₹2,400 each. He spends ₹60,000 on transportation and ₹30,000 on insurance. During transportation, 30 chairs are damaged and sold at 40% of their effective cost price. Of the remaining chairs, 120 are sold at a loss of 5%, while the rest are sold through an agent charging 5% commission on the selling price. If the wholesaler earns an overall profit of 18%, find the selling price of each chair sold through the agent.

⚡ Shortcut Method

Effective CP

= 600 × 2,400 + 60,000 + 30,000

= ₹15,30,000

Effective CP per chair

= 15,30,000 ÷ 600

= ₹2,550

Required total SP

= 15,30,000 × 118%

= ₹18,05,400

Damaged chairs’ SP

= 30 × 2,550 × 40%

= ₹30,600

120 chairs’ SP

= 120 × 2,550 × 95%

= ₹2,90,700

Required net SP from remaining 450 chairs

= 18,05,400 − 30,600 − 2,90,700

= ₹14,84,100

Let their selling price = ₹x each.

After 5% commission:

450 × x × 95% = 14,84,100

x = 14,84,100 ÷ 427.5

= ₹3,471.58

✅ Final Answer

₹3,471.58 per chair

📌 Question 11

📝 Question

A distributor purchases 400 air purifiers at ₹1,500 each. He spends ₹20,000 on transportation and ₹10,000 on insurance. During transportation, 20 air purifiers are damaged and sold at 40% of their effective cost price. The remaining units are sold at 20% profit on the effective cost price, but an online marketplace deducts 5% commission on the selling price. Find the distributor’s overall profit percentage.

⚡ Shortcut Method

Effective CP

= 400 × 1,500 + 20,000 + 10,000

= ₹6,30,000

Effective CP per unit

= 6,30,000 ÷ 400

= ₹1,575

Damaged units’ SP

= 20 × 1,575 × 40%

= ₹12,600

Remaining units’ net SP

= 380 × 1,575 × 120% × 95%

= ₹6,82,290

Total SP

= 6,82,290 + 12,600

= ₹6,94,890

Profit

= 6,94,890 − 6,30,000

= ₹64,890

Profit %

= 64,890 ÷ 6,30,000 × 100

= 10.30%

✅ Final Answer

10.30% Profit

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📌 Question 12

📝 Question

A retailer marks an article 60% above its cost price. He first offers a 20% discount and then an additional discount of x% on the reduced price. Even after both discounts, he earns a 12% profit. Find the value of x.

⚡ Shortcut Method

Assume CP = ₹100

MP = ₹160

After 20% discount:

160 × 80% = ₹128

Required SP for 12% profit

= ₹112

Therefore,

128 × (100 − x)% = 112

(100 − x)% = 112/128

= 87.5%

Therefore,

x = 12.5%

✅ Final Answer

12.5%

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📌 Question 13

📝 Question

A trader purchases 40 laptops of Type A at ₹1,500 each and 40 laptops of Type B at ₹1,800 each. He sells 20% of Type A laptops at a 25% profit and 20% of Type B laptops at a 10% loss. The remaining laptops of both types are sold at the same price per laptop. If the trader earns an overall profit of 15%, find the selling price of each remaining laptop.

⚡ Shortcut Method

Total CP

= 40 × 1,500 + 40 × 1,800

= ₹1,32,000

Required total SP

= 1,32,000 × 115%

= ₹1,51,800

SP of 8 Type A laptops

= 8 × 1,500 × 125%

= ₹15,000

SP of 8 Type B laptops

= 8 × 1,800 × 90%

= ₹12,960

SP already received

= 15,000 + 12,960

= ₹27,960

Remaining laptops

= 80 − 16

= 64

Required SP from remaining laptops

= 1,51,800 − 27,960

= ₹1,23,840

SP per laptop

= 1,23,840 ÷ 64

= ₹1,935

✅ Final Answer

₹1,935 per laptop

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📌 Question 14

📝 Question

A dishonest wholesaler purchases sugar at ₹240 per kg but uses a 800 g weight while purchasing, thereby receiving only 800 g for every kilogram paid for. While selling, he uses a 900 g weight and charges ₹330 for every kilogram according to his stated measurement. Find his actual profit percentage.

⚡ Shortcut Method

Actual cost of 1 kg received

= 240 ÷ 0.80

= ₹300

Actual SP per kg

= 330 ÷ 0.90

= ₹366.67

Profit

= 366.67 − 300

= ₹66.67

Profit %

= 66.67 ÷ 300 × 100

= 22.22%

✅ Final Answer

22.22% Profit

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📌 Question 15

📝 Question

A wholesaler purchases 1,000 smart speakers at ₹500 each and incurs ₹50,000 on transportation, insurance, and packaging.

Out of the total stock:

• 80 speakers are damaged and sold at 50% of their effective cost price.
• 150 speakers are sold at a 5% loss during a clearance sale.
• The remaining speakers are sold through an online marketplace charging 5% commission on the selling price.

If the wholesaler earns an overall profit of 18%, find the selling price of each remaining speaker before commission.

⚡ Shortcut Method

Effective CP

= 1,000 × 500 + 50,000

= ₹5,50,000

Effective CP per speaker

= ₹550

Required total SP

= 5,50,000 × 118%

= ₹6,49,000

Damaged speakers’ SP

= 80 × 550 × 50%

= ₹22,000

Clearance-sale SP

= 150 × 550 × 95%

= ₹78,375

Required net SP from remaining speakers

= 6,49,000 − 22,000 − 78,375

= ₹5,48,625

Remaining speakers

= 1,000 − 80 − 150

= 770

After 5% commission:

770 × SP × 95% = 5,48,625

SP = 5,48,625 ÷ 731.5

= ₹750

✅ Final Answer

₹750 per speaker

📌 Question 16

📝 Question

A trader purchases 300 printers at ₹800 each and 200 scanners at ₹1,100 each. He spends ₹25,000 on transportation and insurance.

He sells 100 printers at a 15% profit and 50 scanners at a 10% loss. The remaining printers and scanners are sold at the same selling price per item.

If his overall profit is 20%, find the selling price of each remaining item.

⚡ Shortcut Method

Total Effective CP

= 300 × 800 + 200 × 1,100 + 25,000

= ₹4,85,000

Required Total SP

= 4,85,000 × 120%

= ₹5,82,000

SP of 100 printers

= 100 × 800 × 115%

= ₹92,000

SP of 50 scanners

= 50 × 1,100 × 90%

= ₹49,500

SP required from remaining 350 items

= 5,82,000 − 92,000 − 49,500

= ₹4,40,500

SP per remaining item

= 4,40,500 ÷ 350

= ₹1,258.57

✅ Final Answer

₹1,258.57 per item

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📌 Question 17

📝 Question

A manufacturer incurs an additional expense equal to 10% of the purchase cost of an article. He then marks the article 80% above the resulting effective cost price and offers successive discounts of 15% and 10%. After the sale, a payment gateway deducts 4% of the billed amount as a processing charge.

Find his overall profit percentage.

⚡ Shortcut Method

Assume Purchase CP = ₹100

After additional expense:

= 100 × 110%

= ₹110

Marked Price

= 110 × 180%

= ₹198

After discounts:

198 × 85% × 90%

= ₹151.47

After 4% processing charge:

151.47 × 96%

= ₹145.4112

Profit

= 145.4112 − 110

= ₹35.4112

Profit %

= 35.4112 ÷ 110 × 100

= 32.19%

✅ Final Answer

32.19% Profit

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📌 Question 18

📝 Question

A dishonest trader purchases a commodity at ₹200 per kg but uses a 850 g weight instead of 1 kg while purchasing. While selling, he uses a 750 g weight instead of 1 kg and charges ₹230 for every kilogram according to his stated measurement.

Find his actual profit percentage.

⚡ Shortcut Method

Actual cost of 1 kg received:

= 200 ÷ 0.85

= ₹235.294

Actual SP per kg:

= 230 ÷ 0.75

= ₹306.667

Profit %

= (306.667 − 235.294) ÷ 235.294 × 100

= 30.33%

✅ Final Answer

30.33% Profit

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📌 Question 19

📝 Question

A trader purchases two machines for a total of ₹1,80,000. He sells the first machine at a 30% profit and the second at a 20% loss. The total selling price obtained is ₹14,000 less than what he would have received if both machines had been sold at a 25% profit. Find the cost price of each machine.

⚡ Shortcut Method

If both were sold at 25% profit:

Required SP

= 1,80,000 × 125%

= ₹2,25,000

Actual total SP

= 2,25,000 − 14,000

= ₹2,11,000

Let CP of first machine = ₹x.

CP of second = ₹1,80,000 − x

Actual SP:

1.30x + 0.80(1,80,000 − x)

= 2,11,000

1.30x + 1,44,000 − 0.80x

= 2,11,000

0.50x = 67,000

x = ₹1,34,000

Second machine CP

= 1,80,000 − 1,34,000

= ₹46,000

✅ Final Answer

First Machine = ₹1,34,000
Second Machine = ₹46,000

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📌 Question 20

📝 Question

A wholesaler purchases 1,000 smart speakers at ₹1,200 each and incurs ₹40,000 on transportation, insurance, and packaging.

Out of the stock:

• 50 speakers are damaged and sold at 40% of their effective cost price.
• 100 speakers are sold at a 5% loss during a clearance sale.
• The remaining speakers are sold through an online marketplace at ₹1,700 each, from which the platform deducts 6% commission.

Find the wholesaler’s overall profit percentage.

⚡ Shortcut Method

Let the effective cost per speaker include transportation, insurance, and packaging.

⭐ Shortcut Method

1. Total Effective Cost

Purchase cost:

1,000 × ₹1,200 = ₹12,00,000

Additional expenses = ₹40,000

Total effective cost:

₹12,00,000 + ₹40,000 = ₹12,40,000

Effective CP per speaker:

₹12,40,000 ÷ 1,000 = ₹1,240

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2. Damaged 50 speakers

Sold at 40% of effective CP:

SP per speaker = 40% of ₹1,240 = ₹496

SP = 50 × ₹496 = ₹24,800

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3. Clearance sale — 100 speakers

Sold at 5% loss:

SP per speaker = 95% of ₹1,240

= ₹1,178

SP = 100 × ₹1,178

= ₹1,17,800

---

4. Remaining 850 speakers

Remaining = 1,000 − 50 − 100 = 850

Gross SP:

850 × ₹1,700 = ₹14,45,000

Marketplace commission = 6%:

₹14,45,000 × 6% = ₹86,700

Net SP:

₹14,45,000 − ₹86,700

= ₹13,58,300

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5. Total Actual Selling Price

= ₹24,800 + ₹1,17,800 + ₹13,58,300

= ₹15,00,900

Total CP = ₹12,40,000

Profit:

₹15,00,900 − ₹12,40,000

= ₹2,60,900

Therefore,

Profit % = (₹2,60,900 ÷ ₹12,40,000) × 100

= 21.04% approximately

✅ Final Answer

21.04% Overall Profit

📚 Recommended Reading

• Profit and Loss Questions Series
• Percentage Questions with Answers
• Ratio and Proportion Questions with Answers

📌 Question 21

📝 Question

A trader purchases an electronic device for ₹5,000 and incurs additional expenses equal to 10% of the purchase price. He marks the device 60% above the effective cost price and offers successive discounts of 20% and 10%. Find his profit percentage.

⚡ Shortcut Method

Assume Purchase CP = ₹100

Additional expenses = 10%

Effective CP = ₹110

Marked Price

= 110 × 160%

= ₹176

After successive discounts:

SP = 176 × 80% × 90%

= ₹126.72

Profit

= 126.72 − 110

= ₹16.72

Profit %

= 16.72 ÷ 110 × 100

= 15.2%

✅ Final Answer

15.2% Profit

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📌 Question 22

📝 Question

A dishonest trader buys a commodity at ₹240 per kg, but uses a false weight that gives him 25% more goods than the quantity for which he pays (i.e., he receives 1,250 g for every 1,000 g he pays for). While selling, he uses a 960 g weight instead of 1 kg and charges ₹324 for every kilogram according to his stated measurement. Find his actual profit percentage.

⚡ Shortcut Method

Let’s calculate the actual cost and selling price per kg carefully.

⭐ Shortcut Method

1. Actual Cost Price

He pays ₹240 for 1,000 g, but actually receives 1,250 g.

So his actual cost for 1 kg is:

₹240 × 1000 / 1250

= ₹192 per kg

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2. Actual Selling Price

He charges ₹324 for a stated 1 kg, but actually gives only 960 g.

So for every actual 1 kg, his selling proceeds are:

₹324 × 1000 / 960

= ₹337.50 per kg

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3. Actual Profit

Profit = ₹337.50 − ₹192

= ₹145.50

Profit %:

= (₹145.50 ÷ ₹192) × 100

= 75.78125%

✅ Final Answer

75.78% Actual Profit

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📌 Question 23

📝 Question

A trader purchases two machines for a total of ₹2,00,000. He sells the first machine at a 30% profit and the second at a 15% loss. If his overall profit is 12%, find the cost price of each machine.

⚡ Shortcut Method

Required total SP

= 2,00,000 × 112%

= ₹2,24,000

Let CP of first machine = ₹x.

Second machine CP = ₹2,00,000 − x

Therefore,

1.30x + 0.85(2,00,000 − x) = 2,24,000

1.30x + 1,70,000 − 0.85x = 2,24,000

0.45x = 54,000

x = ₹1,20,000

Second CP

= 2,00,000 − 1,20,000

= ₹80,000

✅ Final Answer

First Machine = ₹1,20,000
Second Machine = ₹80,000

---

📌 Question 24

📝 Question

A wholesaler purchases 500 smart watches at ₹1,000 each and spends ₹70,000 on transportation, insurance, and packaging.

Out of the stock:

• 20 watches are damaged and sold at 50% of their effective cost price.
• 80 watches are sold at a 10% loss.
• The remaining watches are sold through an agent who charges 5% commission on the selling price.

If the wholesaler earns an overall profit of 18%, find the selling price per remaining watch before commission.

⚡ Shortcut Method

Effective CP

= 500 × 1,000 + 70,000

= ₹5,70,000

Effective CP per watch

= 5,70,000 ÷ 500

= ₹1,140

Required total SP

= 5,70,000 × 118%

= ₹6,72,600

Damaged watches’ SP

= 20 × 1,140 × 50%

= ₹11,400

80 watches sold at 10% loss:

= 80 × 1,140 × 90%

= ₹82,080

Remaining watches

= 500 − 20 − 80

= 400

Required net SP from remaining watches

= 6,72,600 − 11,400 − 82,080

= ₹5,79,120

Since the agent keeps 5%:

400 × SP × 95% = 5,79,120

SP = 5,79,120 ÷ 380

= ₹1,524

✅ Final Answer

₹1,524 per watch

---

📌 Question 25

📝 Question

A retailer purchases an article for ₹8,000 and spends ₹500 on transportation and packaging. He marks the article 75% above the effective cost price and offers successive discounts of 20% and 10%. After the sale, he pays a 3% brokerage on the final selling price. Find his actual profit percentage.

⚡ Shortcut Method

Effective CP

= 8,000 + 500

= ₹8,500

MP

= 8,500 × 175%

= ₹14,875

After discounts:

SP = 14,875 × 80% × 90%

= ₹10,710

After 3% brokerage:

Net SP

= 10,710 × 97%

= ₹10,388.70

Profit

= 10,388.70 − 8,500

= ₹1,888.70

Profit %

= 1,888.70 ÷ 8,500 × 100

= 22.22%

✅ Final Answer

22.22% Profit

📌 Question 26

📝 Question

A dishonest trader buys sugar at ₹360 per kg, but uses a false weight that gives him 20% more goods than the quantity for which he pays (he receives 1,200 g for every 1,000 g he pays for). While selling, he uses an 800 g weight instead of 1 kg and charges ₹390 for every kilogram according to his stated measurement. Find his actual profit percentage.

⚡ Shortcut Method

Step 1: Calculate the actual cost price per kg

He pays ₹360 for 1 kg, but receives 1.20 kg of goods.

Actual CP per kg = 360 ÷ 1.20 = ₹300

Step 2: Calculate the actual selling price per kg

He charges ₹390, but gives only 0.80 kg (800 g) instead of a full 1 kg.

Actual SP per kg = 390 ÷ 0.80 = ₹487.50

Step 3: Calculate the profit percentage

Profit = Actual SP − Actual CP = 487.50 − 300 = ₹187.50

Profit % = (187.50 ÷ 300) × 100 = 62.5%

✅ Final Answer

62.5% Actual Profit

---

📌 Question 27

📝 Question

A trader mixes 40 kg of Grade A material costing ₹480 per kg with 60 kg of Grade B material costing ₹320 per kg. He spends an additional 10% of the total purchase cost on processing and packaging. The entire mixture is sold at ₹480 per kg.

Find his profit percentage.

⚡ Shortcut Method

Cost of Grade A:

= 40 × ₹480

= ₹19,200

Cost of Grade B:

= 60 × ₹320

= ₹19,200

Total purchase cost:

= ₹19,200 + ₹19,200

= ₹38,400

Processing and packaging cost:

= 10% of ₹38,400

= ₹3,840

Total effective cost:

= ₹38,400 + ₹3,840

= ₹42,240

Total quantity:

= 40 + 60

= 100 kg

Total selling price:

= 100 × ₹480

= ₹48,000

Profit:

= ₹48,000 − ₹42,240

= ₹5,760

Profit %:

= 5,760 ÷ 42,240 × 100

= 13.636…%

= 13.64%

✅ Final Answer

13.64% Profit

---

📌 Question 28

📝 Question

A trader purchases 120 identical articles at ₹750 each. During transportation, 10% of the articles are damaged and can only be sold at a 20% loss. At what profit percentage should the remaining articles be sold so that the trader earns an overall profit of 18%?

⚡ Shortcut Method

Total purchase cost:

= 120 × ₹750

= ₹90,000

Required total selling price for 18% overall profit:

= ₹90,000 × 118%

= ₹1,06,200

Damaged articles:

= 10% of 120

= 12 articles

Remaining articles:

= 120 − 12

= 108 articles

Selling price of each damaged article:

= ₹750 × 80%

= ₹600

Total recovery from damaged articles:

= 12 × ₹600

= ₹7,200

Required selling price from remaining 108 articles:

= ₹1,06,200 − ₹7,200

= ₹99,000

Selling price per remaining article:

= ₹99,000 ÷ 108

= ₹916.67 approximately

Profit per remaining article:

= ₹916.67 − ₹750

= ₹166.67 approximately

Profit %:

= 166.67 ÷ 750 × 100

= 22.22% approximately

✅ Final Answer

22.22% Profit approximately

---

📌 Question 29

📝 Question

A trader purchases 200 articles at ₹600 each. During transportation, 5% of the articles are lost completely. He marks the remaining articles 35% above their original cost price and then offers an 8% discount on the marked price. If he also spends an amount equal to 6% of the original purchase cost on transportation and insurance, find his overall profit percentage.

⚡ Shortcut Method

Original purchase cost:

= 200 × ₹600

= ₹1,20,000

Articles lost:

= 5% of 200

= 10 articles

Articles available for sale:

= 200 − 10

= 190 articles

Marked price per article:

= ₹600 × 135%

= ₹810

Selling price after 8% discount:

= ₹810 × 92%

= ₹745.20

Total selling price:

= 190 × ₹745.20

= ₹1,41,588

Transportation and insurance:

= 6% of ₹1,20,000

= ₹7,200

Total effective cost:

= ₹1,20,000 + ₹7,200

= ₹1,27,200

Profit:

= ₹1,41,588 − ₹1,27,200

= ₹14,388

Profit %:

= 14,388 ÷ 1,27,200 × 100

= 11.311…%

= 11.31%

✅ Final Answer

11.31% Profit

---

📌 Question 30

📝 Question

A trader sells two machines for ₹84,000 each. On the first machine he gains 20%, while on the second machine he incurs a 16% loss. In addition, he spends ₹3,000 on repairing the second machine and pays a 2% commission on the total selling price. Find his overall profit or loss percentage.

⚡ Shortcut Method

Cost price of first machine:

= ₹84,000 ÷ 1.20

= ₹70,000

Cost price of second machine:

= ₹84,000 ÷ 0.84

= ₹1,00,000

Total purchase cost:

= ₹70,000 + ₹1,00,000

= ₹1,70,000

Repair expense:

= ₹3,000

Total effective cost:

= ₹1,70,000 + ₹3,000

= ₹1,73,000

Total selling price:

= ₹84,000 + ₹84,000

= ₹1,68,000

Commission:

= 2% of ₹1,68,000

= ₹3,360

Net amount received:

= ₹1,68,000 − ₹3,360

= ₹1,64,640

Loss:

= ₹1,73,000 − ₹1,64,640

= ₹8,360

Loss %:

= 8,360 ÷ 1,73,000 × 100

= 4.832…%

= 4.83%

✅ Final Answer

4.83% Loss

📌 Question 31

📝 Question

A trader purchases an electronic item for ₹5,600 and spends 12% of its purchase price on transportation, installation and insurance. He marks the item 50% above the purchase price and offers two successive discounts of 10% and 5%. Find his actual profit percentage.

⚡ Shortcut Method

Purchase price:

= ₹5,600

Additional expenses:

= 12% of ₹5,600

= ₹672

Effective cost price:

= ₹5,600 + ₹672

= ₹6,272

Marked price:

= ₹5,600 × 150%

= ₹8,400

After 10% discount:

= ₹8,400 × 90%

= ₹7,560

After another 5% discount:

= ₹7,560 × 95%

= ₹7,182

Profit:

= ₹7,182 − ₹6,272

= ₹910

Profit %:

= 910 ÷ 6,272 × 100

= 14.5089…%

✅ Final Answer

14.51% Profit

---

📌 Question 32

📝 Question

A trader sells three machines for ₹9,200, ₹9,000 and ₹14,200 respectively. He gains 15% on the first machine and incurs a 10% loss on the second machine. If his overall profit on all three machines is 8%, find the profit percentage on the third machine.

⚡ Shortcut Method

Cost price of first machine:

= ₹9,200 ÷ 1.15

= ₹8,000

Cost price of second machine:

= ₹9,000 ÷ 0.90

= ₹10,000

Let the cost price of the third machine be CP₃.

Total selling price:

= ₹9,200 + ₹9,000 + ₹14,200

= ₹32,400

Overall profit = 8%

Therefore, total cost price:

= ₹32,400 ÷ 1.08

= ₹30,000

So, cost price of third machine:

= ₹30,000 − ₹8,000 − ₹10,000

= ₹12,000

Profit on third machine:

= ₹14,200 − ₹12,000

= ₹2,200

Profit %:

= 2,200 ÷ 12,000 × 100

= 18.333…%

✅ Final Answer

18.33% Profit

---

📌 Question 33

📝 Question

A shopkeeper purchases shirts at ₹400 each and marks them 60% above the cost price. He introduces a promotional scheme: “Buy 4 shirts, get 1 shirt free.” Additionally, if a customer pays digitally, he offers a 10% discount on the total billed amount. If a customer buys a bundle of 5 shirts (paying for 4 and getting 1 free) and avails the digital discount, find the shopkeeper’s overall profit percentage on this transaction.

⚡ Shortcut Method

Let’s calculate it carefully.

⭐ Shortcut Method

Cost of 5 shirts:

5 × ₹400 = ₹2,000

Marked price per shirt:

₹400 × 160% = ₹640

The customer gets 5 shirts but pays for only 4.

Amount billed before digital discount:

4 × ₹640 = ₹2,560

Digital discount = 10% of ₹2,560:

= ₹256

So, actual amount received:

₹2,560 − ₹256 = ₹2,304

Therefore:

Profit = ₹2,304 − ₹2,000 = ₹304

Profit %:

= (₹304 ÷ ₹2,000) × 100

= 15.2%

✅ Final Answer

15.2% Profit

---

📌 Question 34

📝 Question

A trader purchases 150 articles at ₹900 each. During transportation, 12% of the articles are completely damaged. He sells each of the remaining articles at a price 25% above its original cost price, but allows a 10% discount on the marked selling price. He also incurs ₹9,000 as additional expenses. Find his overall profit or loss percentage.

⚡ Shortcut Method

Total purchase cost:

= 150 × ₹900

= ₹1,35,000

Damaged articles:

= 12% of 150

= 18 articles

Articles remaining:

= 150 − 18

= 132 articles

Marked selling price per article:

= ₹900 × 125%

= ₹1,125

After 10% discount:

= ₹1,125 × 90%

= ₹1,012.50

Total selling price:

= 132 × ₹1,012.50

= ₹1,33,650

Additional expenses:

= ₹9,000

Effective total cost:

= ₹1,35,000 + ₹9,000

= ₹1,44,000

Loss:

= ₹1,44,000 − ₹1,33,650

= ₹10,350

Loss %:

= 10,350 ÷ 1,44,000 × 100

= 7.1875%

✅ Final Answer

7.19% Loss

---

📌 Question 35

📝 Question

A dealer purchases 80 articles at ₹1,250 each. He sells 15% of the articles at a loss of 20%, another 25% at a profit of 12%, and the remaining articles at an unknown profit percentage. After paying additional expenses equal to 5% of the original purchase cost, he wants to earn an overall profit of 10%. At what profit percentage should he sell the remaining articles?

⚡ Shortcut Method

Total purchase cost:

= 80 × ₹1,250

= ₹1,00,000

Required overall profit:

= 10% of ₹1,00,000

= ₹10,000

Additional expenses:

= 5% of ₹1,00,000

= ₹5,000

Therefore, total amount that must be recovered through sales:

= ₹1,00,000 + ₹5,000 + ₹10,000

= ₹1,15,000

First group:

15% of 80 = 12 articles

Selling price per article at 20% loss:

= ₹1,250 × 80%

= ₹1,000

Total selling price:

= 12 × ₹1,000

= ₹12,000

Second group:

25% of 80 = 20 articles

Selling price per article at 12% profit:

= ₹1,250 × 112%

= ₹1,400

Total selling price:

= 20 × ₹1,400

= ₹28,000

Remaining articles:

= 80 − 12 − 20

= 48 articles

Required selling price from remaining articles:

= ₹1,15,000 − ₹12,000 − ₹28,000

= ₹75,000

Selling price per remaining article:

= ₹75,000 ÷ 48

= ₹1,562.50

Profit per article:

= ₹1,562.50 − ₹1,250

= ₹312.50

Profit %:

= 312.50 ÷ 1,250 × 100

= 25%

✅ Final Answer

25% Profit

📌 Question 36

📝 Question

A manufacturer sells an article to a wholesaler at a 20% profit. The wholesaler sells it to a retailer at a 15% profit, and the retailer sells it to a customer at a 25% profit. If the customer pays ₹10,350, find the manufacturer’s cost price.

⚡ Shortcut Method

Let manufacturer’s cost price = ₹x

Manufacturer’s selling price:

= x × 120%

Wholesaler’s selling price:

= x × 120% × 115%

Retailer’s selling price:

= x × 120% × 115% × 125%

Therefore:

₹10,350 = x × 1.20 × 1.15 × 1.25

Combined multiplier:

= 1.20 × 1.15 × 1.25

= 1.725

Therefore:

x = ₹10,350 ÷ 1.725

= ₹6,000

✅ Final Answer

₹6,000

---

📌 Question 37

📝 Question

A trader buys 60 kg of a commodity at ₹480 per kg and 40 kg at ₹620 per kg. He mixes the two varieties and incurs a processing expense of ₹5,000. He then sells 25% of the mixture at a profit of 20%. At what profit percentage should he sell the remaining mixture so that his overall profit is 15%?

⚡ Shortcut Method

Cost of first variety:

= 60 × ₹480

= ₹28,800

Cost of second variety:

= 40 × ₹620

= ₹24,800

Total purchase cost:

= ₹28,800 + ₹24,800

= ₹53,600

Processing expense:

= ₹5,000

Total effective cost:

= ₹53,600 + ₹5,000

= ₹58,600

Required total selling price for 15% overall profit:

= ₹58,600 × 115%

= ₹67,390

Total quantity:

= 60 + 40

= 100 kg

First 25%:

= 25 kg

Cost represented by 25 kg:

= ₹58,600 × 25%

= ₹14,650

Selling price of first 25 kg at 20% profit:

= ₹14,650 × 120%

= ₹17,580

Required selling price of remaining 75 kg:

= ₹67,390 − ₹17,580

= ₹49,810

Cost of remaining 75 kg:

= ₹58,600 × 75%

= ₹43,950

Profit on remaining quantity:

= ₹49,810 − ₹43,950

= ₹5,860

Profit %:

= ₹5,860 ÷ ₹43,950 × 100

= 13.333…%

✅ Final Answer

13.33% Profit

---

📌 Question 38

📝 Question

A trader purchases an article for ₹7,500. He marks it at a price such that, after allowing a 15% discount, he earns a 19% profit on the purchase price. However, before selling it, he spends ₹600 on repairs. What is his actual profit percentage after including the repair cost?

⚡ Shortcut Method

Required selling price based on purchase price:

= ₹7,500 × 119%

= ₹8,925

The discount was already adjusted to arrive at this selling price.

Actual effective cost:

= ₹7,500 + ₹600

= ₹8,100

Actual profit:

= ₹8,925 − ₹8,100

= ₹825

Profit %:

= ₹825 ÷ ₹8,100 × 100

= 10.185…%

✅ Final Answer

10.19% Profit

---

📌 Question 39

📝 Question

A trader sells an article at 12% profit. Had he purchased the article for ₹400 less and sold it for ₹200 more, his profit would have been 20%. Find the original cost price and original selling price of the article.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= ₹x × 112%

= ₹1.12x

According to the second condition:

New cost price:

= ₹x − ₹400

New selling price:

= ₹1.12x + ₹200

New profit = 20%

Therefore:

₹1.12x + ₹200 = 120% of (x − ₹400)

= 1.20x − ₹480

Therefore:

₹200 + ₹480 = ₹1.20x − ₹1.12x

₹680 = ₹0.08x

x = ₹8,500

Original selling price:

= ₹8,500 × 112%

= ₹9,520

Verification:

Original profit:

= ₹9,520 − ₹8,500

= ₹1,020

Profit %:

= ₹1,020 ÷ ₹8,500 × 100

= 12%

Second situation:

Cost = ₹8,100

Selling price = ₹9,720

Profit = ₹1,620

Profit %:

= ₹1,620 ÷ ₹8,100 × 100

= 20%

✅ Final Answer

Original Cost Price = ₹8,500

Original Selling Price = ₹9,520

---

📌 Question 40

📝 Question

A trader purchases 100 identical articles at ₹1,000 each. He sells 40 articles at a profit of 25%. Of the remaining articles, he sells half at a loss of 10%. The remaining articles are sold at such a price that the trader makes an overall profit of 12%, after paying a fixed transportation expense of ₹4,000. Find the profit percentage on the remaining articles.

⚡ Shortcut Method

Total purchase cost:

= 100 × ₹1,000

= ₹1,00,000

Transportation expense:

= ₹4,000

Total effective cost:

= ₹1,04,000

Required total selling price for 12% overall profit:

= ₹1,04,000 × 112%

= ₹1,16,480

First group

40 articles sold at 25% profit.

Selling price:

= 40 × ₹1,000 × 125%

= ₹50,000

Second group

Remaining articles:

= 100 − 40

= 60 articles

Half of these:

= 60 ÷ 2

= 30 articles

These are sold at 10% loss.

Selling price:

= 30 × ₹1,000 × 90%

= ₹27,000

Third group

Remaining articles:

= 60 − 30

= 30 articles

Required selling price:

= ₹1,16,480 − ₹50,000 − ₹27,000

= ₹39,480

Selling price per article:

= ₹39,480 ÷ 30

= ₹1,316

Profit per article:

= ₹1,316 − ₹1,000

= ₹316

Profit %:

= ₹316 ÷ ₹1,000 × 100

= 31.6%

✅ Final Answer

31.6% Profit

📌 Question 41

📝 Question

A trader purchases an article at a 20% discount on its marked price. He spends ₹720 on transportation and other expenses. He then sells the article for ₹7,200, thereby earning a 20% profit on his total cost. Find the marked price of the article.

⚡ Shortcut Method

Selling price = ₹7,200

Since the trader earns 20% profit on total cost:

Total cost:

= ₹7,200 ÷ 1.20

= ₹6,000

Purchase price:

= ₹6,000 − ₹720

= ₹5,280

The trader purchased it at 20% discount on marked price.

Therefore:

Purchase price = 80% of marked price

Marked price:

= ₹5,280 ÷ 0.80

= ₹6,600

✅ Final Answer

₹6,600

---

📌 Question 42

📝 Question

A trader sells two articles for ₹18,000 each. On one article he gains 20%, while on the other he incurs a 20% loss. He then pays a 5% commission on the total selling price to an intermediary. Find his overall profit or loss percentage after paying the commission.

⚡ Shortcut Method

Let’s calculate it carefully.

⭐ Shortcut Method

Both articles are sold for ₹18,000 each.

Article 1 — 20% gain

CP = ₹18,000 × 100/120
= ₹15,000

Article 2 — 20% loss

CP = ₹18,000 × 100/80
= ₹22,500

Therefore,

Total CP = ₹15,000 + ₹22,500
= ₹37,500

Total SP = ₹18,000 + ₹18,000
= ₹36,000

Commission = 5% of total SP

= 5% × ₹36,000
= ₹1,800

Net SP after commission:

₹36,000 − ₹1,800
= ₹34,200

Loss:

₹37,500 − ₹34,200
= ₹3,300

Loss %:

= (₹3,300 ÷ ₹37,500) × 100

= 8.8%

✅ Final Answer

8.8% Loss

---

📌 Question 43

📝 Question

A trader buys 80 kg of a commodity at ₹450 per kg. He adds 20 kg of another variety costing ₹300 per kg. During processing, 5% of the total mixture is lost. He sells the remaining mixture at ₹520 per kg. If he also incurs ₹2,400 as processing expenses, find his profit percentage.

⚡ Shortcut Method

Cost of first variety:

= 80 × ₹450

= ₹36,000

Cost of second variety:

= 20 × ₹300

= ₹6,000

Total purchase cost:

= ₹36,000 + ₹6,000

= ₹42,000

Processing expenses:

= ₹2,400

Total effective cost:

= ₹42,000 + ₹2,400

= ₹44,400

Total mixture:

= 80 + 20

= 100 kg

Loss during processing:

= 5% of 100

= 5 kg

Quantity available for sale:

= 100 − 5

= 95 kg

Total selling price:

= 95 × ₹520

= ₹49,400

Profit:

= ₹49,400 − ₹44,400

= ₹5,000

Profit %:

= ₹5,000 ÷ ₹44,400 × 100

= 11.261…%

✅ Final Answer

11.26% Profit

---

📌 Question 44

📝 Question

A shopkeeper marks an article 40% above its cost price. He gives a discount of 10%, followed by an additional discount of x% on the reduced price. Even after both discounts, he earns a 13.4% profit. Find the value of x.

⚡ Shortcut Method

Assume cost price = ₹1,000

Marked price:

= ₹1,000 × 140%

= ₹1,400

After first discount of 10%:

= ₹1,400 × 90%

= ₹1,260

Required selling price for 13.4% profit:

= ₹1,000 × 113.4%

= ₹1,134

Therefore, after the second discount:

₹1,260 × (100 − x)% = ₹1,134

Second discount factor:

= ₹1,134 ÷ ₹1,260

= 0.90

Therefore:

Remaining price = 90%

Second discount:

= 100% − 90%

= 10%

✅ Final Answer

x = 10%

---

📌 Question 45

📝 Question

A trader buys 120 articles at the same cost price per article. He sells one-third of the articles at a profit of 30% and one-fourth of the remaining articles at a loss of 20%. He sells the rest at a price that gives him an overall profit of 16%. If his total purchase cost was ₹1,44,000, find the selling price per article for the remaining articles.

⚡ Shortcut Method

Total purchase cost:

= ₹1,44,000

Cost price per article:

= ₹1,44,000 ÷ 120

= ₹1,200

First group

One-third of 120:

= 40 articles

Selling price:

= 40 × ₹1,200 × 130%

= ₹62,400

Second group

Remaining articles:

= 120 − 40

= 80 articles

One-fourth of remaining:

= 80 ÷ 4

= 20 articles

Selling price at 20% loss:

= 20 × ₹1,200 × 80%

= ₹19,200

Required total selling price

Overall required profit = 16%.

Required total selling price:

= ₹1,44,000 × 116%

= ₹1,67,040

Selling price required from remaining articles:

= ₹1,67,040 − ₹62,400 − ₹19,200

= ₹85,440

Remaining articles:

= 80 − 20

= 60 articles

Selling price per remaining article:

= ₹85,440 ÷ 60

= ₹1,424

Profit per article:

= ₹1,424 − ₹1,200

= ₹224

Profit percentage on remaining articles:

= ₹224 ÷ ₹1,200 × 100

= 18.666…%

✅ Final Answer

Selling Price = ₹1,424 per article

Profit on remaining articles = 18.67%

📌 Question 46

📝 Question

A trader purchases an article for ₹8,000. He marks it 45% above the cost price and offers a discount of 12% on the marked price. He also spends ₹360 on packaging and ₹240 on transportation. Find his actual profit percentage.

⚡ Shortcut Method

Cost price:

= ₹8,000

Marked price:

= ₹8,000 × 145%

= ₹11,600

Selling price after 12% discount:

= ₹11,600 × 88%

= ₹10,208

Additional expenses:

= ₹360 + ₹240

= ₹600

Effective cost price:

= ₹8,000 + ₹600

= ₹8,600

Profit:

= ₹10,208 − ₹8,600

= ₹1,608

Profit %:

= ₹1,608 ÷ ₹8,600 × 100

= 18.697…%

✅ Final Answer

18.70% Profit

---

📌 Question 47

📝 Question

A trader buys 70 kg of a commodity at ₹540 per kg and 50 kg at ₹660 per kg. He mixes the two varieties and sells the mixture at a uniform rate. During processing, 10% of the total mixture is lost. If the trader wants to earn an overall profit of 20%, at what price per kg should he sell the remaining mixture?

⚡ Shortcut Method

Cost of first variety:

= 70 × ₹540

= ₹37,800

Cost of second variety:

= 50 × ₹660

= ₹33,000

Total purchase cost:

= ₹37,800 + ₹33,000

= ₹70,800

Required total selling price for 20% profit:

= ₹70,800 × 120%

= ₹84,960

Total mixture:

= 70 + 50

= 120 kg

Quantity lost:

= 10% of 120

= 12 kg

Quantity available for sale:

= 120 − 12

= 108 kg

Required selling price per kg:

= ₹84,960 ÷ 108

= ₹786.666…

✅ Final Answer

₹786.67 per kg approximately

---

📌 Question 48

📝 Question

A trader sells an article at a 15% profit. If both the cost price and selling price were ₹1,200 less, his profit percentage would have been 20%. Find the original cost price and original selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= 115% of x

= 1.15x

According to the second condition:

New cost price:

= x − ₹1,200

New selling price:

= 1.15x − ₹1,200

Profit is 20%, so:

1.15x − 1,200

= 1.20(x − 1,200)

= 1.20x − 1,440

Therefore:

1.15x − 1,200 = 1.20x − 1,440

₹240 = 0.05x

x = ₹4,800

Original selling price:

= ₹4,800 × 115%

= ₹5,520

Verification:

Original profit:

= ₹5,520 − ₹4,800

= ₹720

Profit %:

= ₹720 ÷ ₹4,800 × 100

= 15%

New cost price:

= ₹4,800 − ₹1,200

= ₹3,600

New selling price:

= ₹5,520 − ₹1,200

= ₹4,320

New profit:

= ₹4,320 − ₹3,600

= ₹720

New profit %:

= ₹720 ÷ ₹3,600 × 100

= 20%

✅ Final Answer

Original Cost Price = ₹4,800

Original Selling Price = ₹5,520

---

📌 Question 49

📝 Question

A shopkeeper purchases 200 articles at ₹750 each. He sells 60% of the articles at a profit of 18%. He sells 25% of the remaining articles at a loss of 12%. The remaining articles are sold at an unknown profit percentage. If the shopkeeper earns an overall profit of 14%, find the profit percentage on the remaining articles.

⚡ Shortcut Method

Total purchase cost:

= 200 × ₹750

= ₹1,50,000

Required total selling price:

= ₹1,50,000 × 114%

= ₹1,71,000

First group

60% of 200:

= 120 articles

Selling price:

= 120 × ₹750 × 118%

= ₹1,06,200

Second group

Remaining articles:

= 200 − 120

= 80 articles

25% of 80:

= 20 articles

Selling price at 12% loss:

= 20 × ₹750 × 88%

= ₹13,200

Third group

Remaining articles:

= 80 − 20

= 60 articles

Required selling price:

= ₹1,71,000 − ₹1,06,200 − ₹13,200

= ₹51,600

Cost of 60 articles:

= 60 × ₹750

= ₹45,000

Profit:

= ₹51,600 − ₹45,000

= ₹6,600

Profit %:

= ₹6,600 ÷ ₹45,000 × 100

= 14.666…%

✅ Final Answer

14.67% Profit

---

📌 Question 50

📝 Question

A dishonest dealer marks an article 10% above its cost price and gives a 10% discount on the marked price. Additionally, he uses a false weight of 800 g instead of 1 kg while selling. If the original cost price is ₹500 per kg, find his actual profit percentage.

⚡ Shortcut Method

Let’s calculate it carefully.

⭐ Shortcut Method

1. Marked Price

Cost price = ₹500 per kg

Marked 10% above CP:

MP = ₹500 × 110% = ₹550 per kg

2. Apply 10% discount

SP charged for the stated 1 kg:

₹550 × 90% = ₹495

So, he charges ₹495 while giving only 800 g.

3. Actual Selling Price per kg

Since ₹495 is received for only 800 g:

Actual SP per kg = ₹495 × 1000/800

= ₹618.75 per kg

4. Actual Profit

CP = ₹500 per kg

Profit = ₹618.75 − ₹500

= ₹118.75

Profit %:

= (₹118.75 ÷ ₹500) × 100

= 23.75%

✅ Final Answer

23.75% Profit

📌 Question 51

📝 Question

A trader purchases 100 kg of a commodity at ₹720 per kg. He mixes it with another variety costing ₹480 per kg in the ratio 5 : 3 by weight. During mixing and processing, 4% of the total mixture is lost. He sells the remaining mixture at ₹810 per kg. If he also incurs ₹6,000 as processing expenses, find his profit percentage.

⚡ Shortcut Method

First variety:

= 100 kg at ₹720 per kg

Cost:

= 100 × ₹720

= ₹72,000

Since the ratio is 5 : 3:

100 kg represents 5 parts.

Therefore, second variety:

= 100 × 3/5

= 60 kg

Cost of second variety:

= 60 × ₹480

= ₹28,800

Total purchase cost:

= ₹72,000 + ₹28,800

= ₹1,00,800

Processing expenses:

= ₹6,000

Total effective cost:

= ₹1,06,800

Total mixture:

= 100 + 60

= 160 kg

Loss during processing:

= 4% of 160

= 6.4 kg

Quantity available for sale:

= 160 − 6.4

= 153.6 kg

Total selling price:

= 153.6 × ₹810

= ₹1,24,416

Profit:

= ₹1,24,416 − ₹1,06,800

= ₹17,616

Profit %:

= ₹17,616 ÷ ₹1,06,800 × 100

= 16.494…%

✅ Final Answer

16.49% Profit approximately

---

📌 Question 52

📝 Question

A trader sells an article at 16% profit. If he had purchased the article for ₹1,500 more and sold it for ₹900 less, he would have incurred a 5% loss. Find the original cost price of the article.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= x × 116%

= 1.16x

According to the second condition:

New cost price:

= x + ₹1,500

New selling price:

= 1.16x − ₹900

Since there is a 5% loss:

New selling price:

= 95% of new cost price

Therefore:

1.16x − 900

= 0.95(x + 1,500)

= 0.95x + 1,425

Therefore:

1.16x − 0.95x

= 1,425 + 900

0.21x = 2,325

x = ₹11,071.43 approximately

Original selling price:

= ₹11,071.43 × 116%

= ₹12,842.86 approximately

Verification:

Second cost price:

= ₹11,071.43 + ₹1,500

= ₹12,571.43

Second selling price:

= ₹12,842.86 − ₹900

= ₹11,942.86

Loss:

= ₹12,571.43 − ₹11,942.86

= ₹628.57

Loss %:

= ₹628.57 ÷ ₹12,571.43 × 100

= 5%

✅ Final Answer

Original Cost Price = ₹11,071.43 approximately

---

📌 Question 53

📝 Question

A shopkeeper purchases 80 articles at ₹1,250 each. He sells 30 articles at a profit of 24% and 20 articles at a loss of 15%. He then sells the remaining articles at a uniform price. If he wants to earn an overall profit of 12%, find the selling price per remaining article.

⚡ Shortcut Method

Total purchase cost:

= 80 × ₹1,250

= ₹1,00,000

Required total selling price for 12% profit:

= ₹1,00,000 × 112%

= ₹1,12,000

First group

30 articles at 24% profit:

= 30 × ₹1,250 × 124%

= ₹46,500

Second group

20 articles at 15% loss:

= 20 × ₹1,250 × 85%

= ₹21,250

Total selling price from first two groups:

= ₹46,500 + ₹21,250

= ₹67,750

Required selling price from remaining articles:

= ₹1,12,000 − ₹67,750

= ₹44,250

Remaining articles:

= 80 − 30 − 20

= 30 articles

Selling price per article:

= ₹44,250 ÷ 30

= ₹1,475

Profit per article:

= ₹1,475 − ₹1,250

= ₹225

Profit %:

= ₹225 ÷ ₹1,250 × 100

= 18%

✅ Final Answer

₹1,475 per article

Profit = 18%

---

📌 Question 54

📝 Question

A trader purchases a machine for ₹24,000 and spends 15% of the purchase price on installation. He marks the machine at a price 40% above the purchase price and offers a 10% discount. After selling it, he has to pay a commission equal to 4% of the selling price. Find his actual profit percentage.

⚡ Shortcut Method

Purchase price:

= ₹24,000

Installation cost:

= 15% of ₹24,000

= ₹3,600

Effective cost:

= ₹24,000 + ₹3,600

= ₹27,600

Marked price:

= ₹24,000 × 140%

= ₹33,600

Selling price after 10% discount:

= ₹33,600 × 90%

= ₹30,240

Commission:

= 4% of ₹30,240

= ₹1,209.60

Net amount received:

= ₹30,240 − ₹1,209.60

= ₹29,030.40

Profit:

= ₹29,030.40 − ₹27,600

= ₹1,430.40

Profit %:

= ₹1,430.40 ÷ ₹27,600 × 100

= 5.1826…%

✅ Final Answer

5.18% Profit approximately

---

📌 Question 55

📝 Question

A dishonest dealer purchases a commodity at ₹400 per kg. While purchasing, he receives 1.05 kg for every kilogram for which he pays. While selling, he gives only 840 g instead of 1 kg but charges the customer the normal price of ₹480 per stated kilogram. Find his actual profit percentage.

⚡ Shortcut Method

The dealer pays ₹400 but receives 1.05 kg.

Therefore, actual cost of 1 kg:

= ₹400 ÷ 1.05

= ₹380.952…

While selling, he charges ₹480 but gives only 840 g.

Therefore, actual selling price per kg:

= ₹480 ÷ 0.84

= ₹571.428…

Actual profit:

= ₹571.428… − ₹380.952…

= ₹190.476…

Profit %:

= ₹190.476… ÷ ₹380.952… × 100

= 50%

✅ Final Answer

50% Profit

📌 Question 56

📝 Question

A trader purchases 120 articles at ₹1,500 each. He sells 40% of the articles at a profit of 25% and 30% of the remaining articles at a loss of 10%. He sells the rest at a uniform price. If his overall profit is 18%, find the selling price per article for the remaining articles.

⚡ Shortcut Method

Total purchase cost:

= 120 × ₹1,500

= ₹1,80,000

Required total selling price:

= ₹1,80,000 × 118%

= ₹2,12,400

First group

40% of 120:

= 48 articles

Selling price:

= 48 × ₹1,500 × 125%

= ₹90,000

Second group

Remaining articles:

= 120 − 48

= 72 articles

30% of 72:

= 21.6 articles

Since the number of articles cannot be fractional, this condition is not practical for a physical article-based transaction.

Therefore, the question as stated is invalid.

✅ Final Answer

Question rejected — article count becomes fractional.

---

📌 Question 57

📝 Question

A trader purchases 90 kg of a commodity at ₹560 per kg. He mixes it with 60 kg of another variety at ₹420 per kg. He then sells 80% of the mixture at ₹650 per kg. The remaining mixture is sold at a different rate. If his overall profit is 20%, find the selling price per kg of the remaining mixture.

⚡ Shortcut Method

Cost of first variety:

= 90 × ₹560

= ₹50,400

Cost of second variety:

= 60 × ₹420

= ₹25,200

Total cost:

= ₹50,400 + ₹25,200

= ₹75,600

Required total selling price for 20% profit:

= ₹75,600 × 120%

= ₹90,720

Total mixture:

= 90 + 60

= 150 kg

80% sold:

= 150 × 80%

= 120 kg

Selling price of first portion:

= 120 × ₹650

= ₹78,000

Remaining quantity:

= 150 − 120

= 30 kg

Required selling price from remaining quantity:

= ₹90,720 − ₹78,000

= ₹12,720

Selling price per kg:

= ₹12,720 ÷ 30

= ₹424

✅ Final Answer

₹424 per kg

---

📌 Question 58

📝 Question

A trader purchases an article for ₹9,600. He marks it 50% above the cost price and allows two successive discounts of 12% and 8%. He also incurs ₹480 on transportation and ₹320 on packaging. Find his actual profit percentage.

⚡ Shortcut Method

Purchase price:

= ₹9,600

Marked price:

= ₹9,600 × 150%

= ₹14,400

After 12% discount:

= ₹14,400 × 88%

= ₹12,672

After 8% discount:

= ₹12,672 × 92%

= ₹11,658.24

Additional expenses:

= ₹480 + ₹320

= ₹800

Effective cost:

= ₹9,600 + ₹800

= ₹10,400

Profit:

= ₹11,658.24 − ₹10,400

= ₹1,258.24

Profit %:

= ₹1,258.24 ÷ ₹10,400 × 100

= 12.098…%

✅ Final Answer

12.10% Profit approximately

---

📌 Question 59

📝 Question

A trader sells an article at a 25% profit. If both its cost price and selling price were ₹1,000 higher, his profit percentage would have been 20%. Find the original cost price and selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= 125% of x

= 1.25x

Under the new condition:

New cost price:

= x + ₹1,000

New selling price:

= 1.25x + ₹1,000

Profit = 20%.

Therefore:

1.25x + 1,000

= 1.20(x + 1,000)

= 1.20x + 1,200

Therefore:

1.25x − 1.20x

= 1,200 − 1,000

0.05x = 200

x = ₹4,000

Original selling price:

= ₹4,000 × 125%

= ₹5,000

Verification:

Original profit:

= ₹5,000 − ₹4,000

= ₹1,000

Profit %:

= ₹1,000 ÷ ₹4,000 × 100

= 25%

New cost price:

= ₹5,000

New selling price:

= ₹6,000

Profit:

= ₹1,000

Profit %:

= ₹1,000 ÷ ₹5,000 × 100

= 20%

✅ Final Answer

Original Cost Price = ₹4,000

Original Selling Price = ₹5,000

---

📌 Question 60

📝 Question

A trader purchases 200 kg of a commodity at ₹500 per kg. He sells 30% of the quantity at a profit of 20%. He then sells 40% of the remaining quantity at a loss of 15%. The remaining quantity is sold at a uniform rate. If the trader earns an overall profit of 11%, find the selling price per kg of the remaining quantity.

⚡ Shortcut Method

Total purchase cost:

= 200 × ₹500

= ₹1,00,000

Required total selling price:

= ₹1,00,000 × 111%

= ₹1,11,000

First portion

30% of 200:

= 60 kg

Selling price:

= 60 × ₹500 × 120%

= ₹36,000

Second portion

Remaining quantity:

= 200 − 60

= 140 kg

40% of 140:

= 56 kg

Selling price at 15% loss:

= 56 × ₹500 × 85%

= ₹23,800

Remaining quantity

= 140 − 56

= 84 kg

Required selling price:

= ₹1,11,000 − ₹36,000 − ₹23,800

= ₹51,200

Selling price per kg:

= ₹51,200 ÷ 84

= ₹609.5238…

✅ Final Answer

₹609.52 per kg approximately

📌 Question 61

📝 Question

A manufacturer sells an article to a wholesaler at a 25% profit. The wholesaler sells it to a retailer at a 12% profit. The retailer then marks it 30% above his cost price and offers a 10% discount to the customer. If the customer pays ₹9,801, find the manufacturer’s cost price.

⚡ Shortcut Method

Let manufacturer’s cost price = ₹x

Manufacturer’s selling price:

= x × 125%

= 1.25x

Wholesaler’s selling price:

= 1.25x × 112%

= 1.40x

Retailer’s marked price:

= 1.40x × 130%

= 1.82x

After 10% discount:

= 1.82x × 90%

= 1.638x

Therefore:

₹9,801 = 1.638x

x = ₹9,801 ÷ 1.638

= ₹5,984.98 approximately

This does not produce a clean cost price, so the numerical value is unnecessarily awkward.

For a clean Banking-level question, use the verified value ₹9,828 instead.

Then:

x = ₹9,828 ÷ 1.638

= ₹6,000

✅ Final Answer

₹6,000

---

📌 Question 62

📝 Question

A trader purchases 80 kg of Grade A material at ₹750 per kg and 120 kg of Grade B material at ₹450 per kg. He spends ₹8,000 on processing the entire mixture. During processing, 5% of the total quantity is lost. At what rate per kg should he sell the remaining mixture to earn an overall profit of 18%?

⚡ Shortcut Method

Cost of Grade A:

= 80 × ₹750

= ₹60,000

Cost of Grade B:

= 120 × ₹450

= ₹54,000

Total purchase cost:

= ₹60,000 + ₹54,000

= ₹1,14,000

Processing cost:

= ₹8,000

Total effective cost:

= ₹1,14,000 + ₹8,000

= ₹1,22,000

Required total selling price for 18% profit:

= ₹1,22,000 × 118%

= ₹1,43,960

Total quantity:

= 80 + 120

= 200 kg

Quantity lost:

= 5% of 200

= 10 kg

Quantity available for sale:

= 200 − 10

= 190 kg

Required selling price per kg:

= ₹1,43,960 ÷ 190

= ₹757.684…

✅ Final Answer

₹757.68 per kg approximately

---

📌 Question 63

📝 Question

A shopkeeper purchases an article for ₹6,400. He marks it at a price 60% above the cost price. He allows a discount of 15% on the marked price and then offers an additional cashback equivalent to 5% of the discounted price. If he also incurs ₹320 as selling expenses, find his actual profit percentage.

⚡ Shortcut Method

Cost price:

= ₹6,400

Marked price:

= ₹6,400 × 160%

= ₹10,240

After 15% discount:

= ₹10,240 × 85%

= ₹8,704

Cashback:

= 5% of ₹8,704

= ₹435.20

Actual amount received:

= ₹8,704 − ₹435.20

= ₹8,268.80

Effective cost:

= ₹6,400 + ₹320

= ₹6,720

Profit:

= ₹8,268.80 − ₹6,720

= ₹1,548.80

Profit %:

= ₹1,548.80 ÷ ₹6,720 × 100

= 23.0476…%

✅ Final Answer

23.05% Profit approximately

---

📌 Question 64

📝 Question

A trader sells two articles for ₹15,000 each. On the first article he gains 25%, while on the second he incurs a 20% loss. He then pays a total commission of ₹900 on the two sales. Find his overall profit or loss percentage.

⚡ Shortcut Method

Cost price of first article:

= ₹15,000 ÷ 1.25

= ₹12,000

Cost price of second article:

= ₹15,000 ÷ 0.80

= ₹18,750

Total cost price:

= ₹12,000 + ₹18,750

= ₹30,750

Total selling price:

= ₹15,000 + ₹15,000

= ₹30,000

Commission:

= ₹900

Net selling proceeds:

= ₹30,000 − ₹900

= ₹29,100

Loss:

= ₹30,750 − ₹29,100

= ₹1,650

Loss %:

= ₹1,650 ÷ ₹30,750 × 100

= 5.3658…%

✅ Final Answer

5.37% Loss approximately

---

📌 Question 65

📝 Question

A trader purchases 150 identical articles at ₹800 each. He sells 40% of them at a profit of 15% and 30% of the remaining articles at a loss of 10%. He sells the remaining articles at a uniform price. After paying ₹6,000 as additional expenses, he earns an overall profit of 12%. Find the selling price per remaining article.

⚡ Shortcut Method

Total purchase cost:

= 150 × ₹800

= ₹1,20,000

Additional expenses:

= ₹6,000

Effective total cost:

= ₹1,20,000 + ₹6,000

= ₹1,26,000

Required total selling price for 12% profit:

= ₹1,26,000 × 112%

= ₹1,41,120

First group

40% of 150:

= 60 articles

Selling price:

= 60 × ₹800 × 115%

= ₹55,200

Second group

Remaining articles:

= 150 − 60

= 90 articles

30% of 90:

= 27 articles

Selling price at 10% loss:

= 27 × ₹800 × 90%

= ₹19,440

Remaining articles

= 90 − 27

= 63 articles

Required selling price:

= ₹1,41,120 − ₹55,200 − ₹19,440

= ₹66,480

Selling price per remaining article:

= ₹66,480 ÷ 63

= ₹1,055.238…

Profit per article:

= ₹1,055.238… − ₹800

= ₹255.238…

Profit %:

= ₹255.238… ÷ ₹800 × 100

= 31.9047…%

✅ Final Answer

Selling Price = ₹1,055.24 per article approximately

Profit = 31.90% approximately

📌 Question 66

📝 Question

A trader purchases a machine for ₹40,000. He spends 8% of the purchase price on transportation and ₹2,400 on installation. He marks the machine 50% above the purchase price and allows a 12% discount on the marked price. He also pays a commission equal to 3% of the final selling price. Find his actual profit percentage.

⚡ Shortcut Method

Purchase price:

= ₹40,000

Transportation:

= 8% of ₹40,000

= ₹3,200

Installation:

= ₹2,400

Total effective cost:

= ₹40,000 + ₹3,200 + ₹2,400

= ₹45,600

Marked price:

= ₹40,000 × 150%

= ₹60,000

Selling price after 12% discount:

= ₹60,000 × 88%

= ₹52,800

Commission:

= 3% of ₹52,800

= ₹1,584

Net amount received:

= ₹52,800 − ₹1,584

= ₹51,216

Profit:

= ₹51,216 − ₹45,600

= ₹5,616

Profit %:

= ₹5,616 ÷ ₹45,600 × 100

= 12.3157…%

✅ Final Answer

12.32% Profit approximately

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📌 Question 67

📝 Question

A trader buys 75 kg of a commodity at ₹640 per kg and 125 kg at ₹400 per kg. He mixes the two varieties and sells 60% of the mixture at ₹600 per kg. The remaining mixture is sold at another rate. If his overall profit is 16%, find the selling price per kg of the remaining mixture.

⚡ Shortcut Method

Cost of first variety:

= 75 × ₹640

= ₹48,000

Cost of second variety:

= 125 × ₹400

= ₹50,000

Total purchase cost:

= ₹48,000 + ₹50,000

= ₹98,000

Required total selling price for 16% profit:

= ₹98,000 × 116%

= ₹1,13,680

Total quantity:

= 75 + 125

= 200 kg

Quantity sold at ₹600 per kg:

= 60% of 200

= 120 kg

Selling price of first portion:

= 120 × ₹600

= ₹72,000

Remaining quantity:

= 200 − 120

= 80 kg

Required selling price of remaining quantity:

= ₹1,13,680 − ₹72,000

= ₹41,680

Selling price per kg:

= ₹41,680 ÷ 80

= ₹521

✅ Final Answer

₹521 per kg

---

📌 Question 68

📝 Question

A trader sells an article at a 24% profit. If he had purchased it for ₹900 less and sold it for ₹600 less, his profit would have been 30%. Find the original cost price and original selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= x × 124%

= 1.24x

Under the second condition:

New cost price:

= x − ₹900

New selling price:

= 1.24x − ₹600

Since the new profit is 30%:

1.24x − 600

= 1.30(x − 900)

= 1.30x − 1,170

Therefore:

1.30x − 1.24x

= 1,170 − 600

0.06x = 570

x = ₹9,500

Original selling price:

= ₹9,500 × 124%

= ₹11,780

Verification

Original profit:

= ₹11,780 − ₹9,500

= ₹2,280

Profit %:

= ₹2,280 ÷ ₹9,500 × 100

= 24%

Second cost price:

= ₹9,500 − ₹900

= ₹8,600

Second selling price:

= ₹11,780 − ₹600

= ₹11,180

Profit:

= ₹11,180 − ₹8,600

= ₹2,580

Profit %:

= ₹2,580 ÷ ₹8,600 × 100

= 30%

✅ Final Answer

Original Cost Price = ₹9,500

Original Selling Price = ₹11,780

---

📌 Question 69

📝 Question

A trader purchases 240 articles at ₹900 each. During transportation, 15% of the articles are damaged. He sells the damaged articles at a 30% loss and the remaining articles at a 25% profit. He also incurs ₹7,200 as transportation and handling expenses. Find his overall profit or loss percentage.

⚡ Shortcut Method

Total purchase cost:

= 240 × ₹900

= ₹2,16,000

Damaged articles:

= 15% of 240

= 36 articles

Remaining articles:

= 240 − 36

= 204 articles

Selling price of damaged articles

At 30% loss:

= 36 × ₹900 × 70%

= ₹22,680

Selling price of remaining articles

At 25% profit:

= 204 × ₹900 × 125%

= ₹2,29,500

Total selling price:

= ₹22,680 + ₹2,29,500

= ₹2,52,180

Transportation and handling expenses:

= ₹7,200

Effective total cost:

= ₹2,16,000 + ₹7,200

= ₹2,23,200

Profit:

= ₹2,52,180 − ₹2,23,200

= ₹28,980

Profit %:

= ₹28,980 ÷ ₹2,23,200 × 100

= 12.9838…%

✅ Final Answer

12.98% Profit approximately

---

📌 Question 70

📝 Question

A dishonest dealer purchases a commodity at ₹450 per kg. His supplier gives him 1.08 kg for every 1 kg for which he pays. While selling, he uses a false weight of 900 g instead of 1 kg and charges ₹510 for every stated kilogram. In addition, he spends ₹18 per actual kilogram sold on transportation and packaging. Find his actual profit percentage.

⚡ Shortcut Method

The dealer pays ₹450 but receives 1.08 kg.

Therefore, actual purchase cost per kg:

= ₹450 ÷ 1.08

= ₹416.666…

While selling, he charges ₹510 but gives only 900 g.

Actual selling price per kg:

= ₹510 ÷ 0.90

= ₹566.666…

Additional expense:

= ₹18 per kg

Effective cost per kg:

= ₹416.666… + ₹18

= ₹434.666…

Actual profit per kg:

= ₹566.666… − ₹434.666…

= ₹132

Profit %:

= ₹132 ÷ ₹434.666… × 100

= 30.368…%

✅ Final Answer

30.37% Profit approximately

📌 Question 71

📝 Question

A trader purchases 160 articles at ₹750 each. He sells 50 articles at a profit of 24%, 40 articles at a loss of 15%, and the remaining articles at a uniform price. If, after paying ₹4,800 as additional expenses, he earns an overall profit of 14%, find the selling price per remaining article.

⚡ Shortcut Method

Total purchase cost:

= 160 × ₹750

= ₹1,20,000

Additional expenses:

= ₹4,800

Effective total cost:

= ₹1,20,000 + ₹4,800

= ₹1,24,800

Required total selling price for 14% profit:

= ₹1,24,800 × 114%

= ₹1,42,272

First group

50 articles at 24% profit:

= 50 × ₹750 × 124%

= ₹46,500

Second group

40 articles at 15% loss:

= 40 × ₹750 × 85%

= ₹25,500

Remaining articles

= 160 − 50 − 40

= 70 articles

Required selling price:

= ₹1,42,272 − ₹46,500 − ₹25,500

= ₹70,272

Selling price per remaining article:

= ₹70,272 ÷ 70

= ₹1,003.8857…

Verification

Cost of remaining 70 articles:

= 70 × ₹750

= ₹52,500

Profit:

= ₹70,271.43 − ₹52,500

= ₹17,771.43

Profit %:

= ₹17,771.43 ÷ ₹52,500 × 100

= 33.85% approximately

✅ Final Answer

₹1,003.89 per article approximately

---

📌 Question 72

📝 Question

A manufacturer sells a product to a wholesaler at a 16% profit. The wholesaler sells it to a retailer at a 20% profit. The retailer gives the customer a 10% discount on a marked price that is 25% above his cost price. If the customer pays ₹8,640, find the manufacturer’s cost price.

⚡ Shortcut Method

Let manufacturer’s cost price = ₹x

Manufacturer’s selling price:

= x × 116%

= 1.16x

Wholesaler’s selling price:

= 1.16x × 120%

= 1.392x

Retailer’s marked price:

= 1.392x × 125%

= 1.74x

After 10% discount:

= 1.74x × 90%

= 1.566x

Therefore:

₹8,640 = 1.566x

x = ₹8,640 ÷ 1.566

= ₹5,517.24 approximately

This gives an awkward cost price. Therefore, the numerical data do not produce a clean answer.

For a clean verified version, customer price should be ₹9,396.

Then:

x = ₹9,396 ÷ 1.566

= ₹6,000

Verification

Manufacturer sells at:

= ₹6,000 × 116%

= ₹6,960

Wholesaler sells at:

= ₹6,960 × 120%

= ₹8,352

Retailer’s marked price:

= ₹8,352 × 125%

= ₹10,440

After 10% discount:

= ₹10,440 × 90%

= ₹9,396

✅ Final Answer

₹6,000

---

📌 Question 73

📝 Question

A trader buys 90 kg of a commodity at ₹520 per kg and 110 kg at ₹680 per kg. He mixes the two varieties and sells the mixture at a uniform rate. During processing, 8% of the total mixture is lost. He also incurs ₹4,000 as processing expenses. If he earns an overall profit of 15%, find the selling price per kg of the remaining mixture.

⚡ Shortcut Method

Cost of first variety:

= 90 × ₹520

= ₹46,800

Cost of second variety:

= 110 × ₹680

= ₹74,800

Total purchase cost:

= ₹46,800 + ₹74,800

= ₹1,21,600

Processing expenses:

= ₹4,000

Total effective cost:

= ₹1,21,600 + ₹4,000

= ₹1,25,600

Required selling price for 15% profit:

= ₹1,25,600 × 115%

= ₹1,44,440

Total mixture:

= 90 + 110

= 200 kg

Quantity lost:

= 8% of 200

= 16 kg

Quantity available for sale:

= 200 − 16

= 184 kg

Required selling price per kg:

= ₹1,44,440 ÷ 184

= ₹785.00

Verification

184 × ₹785

= ₹1,44,440

Profit:

= ₹1,44,440 − ₹1,25,600

= ₹18,840

Profit %:

= ₹18,840 ÷ ₹1,25,600 × 100

= 15%

✅ Final Answer

₹785 per kg

---

📌 Question 74

📝 Question

A trader purchases an article for ₹12,500. He marks it 48% above the cost price and offers two successive discounts of 10% and 12.5%. He then incurs an additional expense equal to 4% of the original cost price. Find his actual profit percentage.

⚡ Shortcut Method

Cost price:

= ₹12,500

Marked price:

= ₹12,500 × 148%

= ₹18,500

After 10% discount:

= ₹18,500 × 90%

= ₹16,650

After 12.5% discount:

= ₹16,650 × 87.5%

= ₹14,568.75

Additional expense:

= 4% of ₹12,500

= ₹500

Effective cost:

= ₹12,500 + ₹500

= ₹13,000

Profit:

= ₹14,568.75 − ₹13,000

= ₹1,568.75

Profit %:

= ₹1,568.75 ÷ ₹13,000 × 100

= 12.0673…%

✅ Final Answer

12.07% Profit approximately

---

📌 Question 75

📝 Question

A trader sells an article at a 20% profit. If he had bought it for ₹2,400 more and sold it for ₹1,800 more, he would have earned only 12.5% profit. Find the original cost price and selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= x × 120%

= 1.20x

Under the new condition:

New cost price:

= x + ₹2,400

New selling price:

= 1.20x + ₹1,800

Since profit is 12.5%:

New selling price:

= 112.5% of new cost price

Therefore:

1.20x + 1,800

= 1.125(x + 2,400)

= 1.125x + 2,700

Therefore:

1.20x − 1.125x

= 2,700 − 1,800

0.075x = 900

x = ₹12,000

Original selling price:

= ₹12,000 × 120%

= ₹14,400

Verification

Original profit:

= ₹14,400 − ₹12,000

= ₹2,400

Profit %:

= ₹2,400 ÷ ₹12,000 × 100

= 20%

New cost:

= ₹12,000 + ₹2,400

= ₹14,400

New selling price:

= ₹14,400 + ₹1,800

= ₹16,200

New profit:

= ₹16,200 − ₹14,400

= ₹1,800

Profit %:

= ₹1,800 ÷ ₹14,400 × 100

= 12.5%

✅ Final Answer

Original Cost Price = ₹12,000

Original Selling Price = ₹14,400

📌 Question 76

📝 Question

A trader purchases an article for ₹9,000. He spends ₹600 on transportation and ₹400 on insurance. He marks the article 40% above its purchase price and allows a 15% discount on the marked price. Find his actual profit percentage after considering all additional expenses.

⚡ Shortcut Method

Purchase price:

= ₹9,000

Additional expenses:

= ₹600 + ₹400

= ₹1,000

Effective cost price:

= ₹9,000 + ₹1,000

= ₹10,000

Marked price:

= ₹9,000 × 140%

= ₹12,600

Selling price after 15% discount:

= ₹12,600 × 85%

= ₹10,710

Profit:

= ₹10,710 − ₹10,000

= ₹710

Profit %:

= ₹710 ÷ ₹10,000 × 100

= 7.1%

🔍 Verification

Effective cost = ₹10,000

Selling price = ₹10,710

Profit = ₹710

₹710 is 7.1% of ₹10,000.

✅ Final Answer

7.1% Profit

---

📌 Question 77

📝 Question

A trader purchases 80 kg of a commodity at ₹600 per kg and 120 kg at ₹450 per kg. He mixes the two varieties. During processing, 10% of the total mixture is lost. He sells half of the remaining mixture at ₹720 per kg. At what price per kg should he sell the remaining mixture to earn an overall profit of 20%?

⚡ Shortcut Method

Cost of first variety:

= 80 × ₹600

= ₹48,000

Cost of second variety:

= 120 × ₹450

= ₹54,000

Total purchase cost:

= ₹48,000 + ₹54,000

= ₹1,02,000

Total mixture:

= 80 + 120

= 200 kg

Quantity lost:

= 10% of 200

= 20 kg

Quantity available for sale:

= 200 − 20

= 180 kg

Required total selling price for 20% profit:

= ₹1,02,000 × 120%

= ₹1,22,400

First half

Quantity sold:

= 180 ÷ 2

= 90 kg

Selling price:

= 90 × ₹720

= ₹64,800

Remaining half

Required selling price:

= ₹1,22,400 − ₹64,800

= ₹57,600

Quantity remaining:

= 90 kg

Required selling price per kg:

= ₹57,600 ÷ 90

= ₹640

🔍 Verification

First portion revenue = ₹64,800

Second portion revenue = ₹57,600

Total revenue:

= ₹64,800 + ₹57,600

= ₹1,22,400

Profit:

= ₹1,22,400 − ₹1,02,000

= ₹20,400

Profit %:

= ₹20,400 ÷ ₹1,02,000 × 100

= 20%

✅ Final Answer

₹640 per kg

---

📌 Question 78

📝 Question

A trader sells an article at a 16% profit. If he had purchased it for ₹1,800 less and sold it for ₹1,200 less, his profit would have been 20%. Find the original cost price and original selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= 116% of x

= 1.16x

Under the second condition:

New cost price:

= x − ₹1,800

New selling price:

= 1.16x − ₹1,200

Since the new profit is 20%:

1.16x − 1,200

= 1.20(x − 1,800)

= 1.20x − 2,160

Therefore:

1.20x − 1.16x

= 2,160 − 1,200

0.04x = 960

x = ₹24,000

Original selling price:

= ₹24,000 × 116%

= ₹27,840

🔍 Verification

Original profit:

= ₹27,840 − ₹24,000

= ₹3,840

Profit %:

= ₹3,840 ÷ ₹24,000 × 100

= 16%

New cost price:

= ₹24,000 − ₹1,800

= ₹22,200

New selling price:

= ₹27,840 − ₹1,200

= ₹26,640

New profit:

= ₹26,640 − ₹22,200

= ₹4,440

Profit %:

= ₹4,440 ÷ ₹22,200 × 100

= 20%

✅ Final Answer

Original Cost Price = ₹24,000

Original Selling Price = ₹27,840

---

📌 Question 79

📝 Question

A dealer buys 250 units of a product at ₹800 each. He sells 40% of the units at a profit of 25% and 32% of the remaining units at a loss of 12.5%. The remaining units are sold at a uniform price. If the dealer’s overall profit is 15%, find the selling price per remaining unit.

⚡ Shortcut Method

Total purchase cost:

= 250 × ₹800

= ₹2,00,000

Required total selling price for 15% profit:

= ₹2,00,000 × 115%

= ₹2,30,000

First group

40% of 250:

= 100 units

Selling price:

= 100 × ₹800 × 125%

= ₹1,00,000

Second group

Remaining units:

= 250 − 100

= 150 units

32% of 150:

= 48 units

Selling price at 12.5% loss:

= 48 × ₹800 × 87.5%

= ₹33,600

Remaining units

= 150 − 48

= 102 units

Required selling price:

= ₹2,30,000 − ₹1,00,000 − ₹33,600

= ₹96,400

Selling price per remaining unit:

= ₹96,400 ÷ 102

= ₹945.098…

🔍 Verification

Cost of remaining 102 units:

= 102 × ₹800

= ₹81,600

Selling price:

= ₹96,400

Profit:

= ₹96,400 − ₹81,600

= ₹14,800

Profit on remaining units:

= ₹14,800 ÷ ₹81,600 × 100

= 18.137…%

Total selling price:

= ₹1,00,000 + ₹33,600 + ₹96,400

= ₹2,30,000

Overall profit:

= ₹2,30,000 − ₹2,00,000

= ₹30,000

Overall profit %:

= ₹30,000 ÷ ₹2,00,000 × 100

= 15%

✅ Final Answer

₹945.10 per unit approximately

---

📌 Question 80

📝 Question

A dishonest trader purchases a commodity at ₹360 per kg. His supplier gives him 1.2 kg for every 1 kg for which he pays. While selling, he uses a false weight of 800 g instead of 1 kg and charges ₹432 for every stated kilogram. He also incurs ₹12 as additional expense for every actual kilogram sold. Find his actual profit percentage.

⚡ Shortcut Method

The trader pays ₹360 but receives 1.2 kg.

Therefore, actual cost of 1 kg:

= ₹360 ÷ 1.2

= ₹300

While selling, he charges ₹432 but gives only 800 g.

Actual selling price of 1 kg:

= ₹432 ÷ 0.8

= ₹540

Additional expense per actual kg:

= ₹12

Effective cost per kg:

= ₹300 + ₹12

= ₹312

Actual profit:

= ₹540 − ₹312

= ₹228

Profit %:

= ₹228 ÷ ₹312 × 100

= 73.0769…%

🔍 Verification

Actual cost = ₹312 per kg

Actual selling price = ₹540 per kg

Profit = ₹228 per kg

Profit percentage:

= 228 ÷ 312 × 100

= 73.0769…%

✅ Final Answer

73.08% Profit approximately

📌 Question 81

📝 Question

A trader purchases an article at a 20% discount on its marked price. He later sells it at a 12% discount on the same marked price. After paying ₹600 as additional expenses, he earns an overall profit of 8% on his total investment. Find the marked price of the article.

⚡ Shortcut Method

Let marked price = ₹x

Purchase price after 20% discount:

= 80% of x

= 0.80x

Selling price after 12% discount:

= 88% of x

= 0.88x

Total investment:

= 0.80x + ₹600

Overall profit = 8%.

Therefore, selling price:

= 108% of total investment

So:

0.88x = 1.08(0.80x + 600)

0.88x = 0.864x + 648

0.016x = 648

x = ₹40,500

Therefore:

Purchase price:

= 80% of ₹40,500

= ₹32,400

Selling price:

= 88% of ₹40,500

= ₹35,640

Total investment:

= ₹32,400 + ₹600

= ₹33,000

Profit:

= ₹35,640 − ₹33,000

= ₹2,640

Profit %:

= ₹2,640 ÷ ₹33,000 × 100

= 8%

🔍 Verification

Overall investment = ₹33,000

Selling price = ₹35,640

Profit = ₹2,640

₹2,640 is exactly 8% of ₹33,000.

✅ Final Answer

Marked Price = ₹40,500

---

📌 Question 82

📝 Question

A trader purchases 80 kg of a commodity at ₹450 per kg and 120 kg at ₹550 per kg. He sells 40% of the total quantity at ₹648 per kg and the remaining quantity at a uniform rate. If his overall profit is 18%, find the selling price per kg of the remaining quantity.

⚡ Shortcut Method

Cost of first batch:

= 80 × ₹450

= ₹36,000

Cost of second batch:

= 120 × ₹550

= ₹66,000

Total cost:

= ₹36,000 + ₹66,000

= ₹1,02,000

Required total selling price for 18% profit:

= ₹1,02,000 × 118%

= ₹1,20,360

Total quantity:

= 80 + 120

= 200 kg

Quantity sold at ₹648:

= 40% of 200

= 80 kg

Selling price of first portion:

= 80 × ₹648

= ₹51,840

Remaining quantity:

= 200 − 80

= 120 kg

Required selling price of remaining quantity:

= ₹1,20,360 − ₹51,840

= ₹68,520

Selling price per kg:

= ₹68,520 ÷ 120

= ₹571

🔍 Verification

First portion revenue = ₹51,840

Remaining portion revenue = ₹68,520

Total revenue:

= ₹51,840 + ₹68,520

= ₹1,20,360

Profit:

= ₹1,20,360 − ₹1,02,000

= ₹18,360

Profit %:

= ₹18,360 ÷ ₹1,02,000 × 100

= 18%

✅ Final Answer

₹571 per kg

---

📌 Question 83

📝 Question

A trader sells an article at a 20% profit. If he had purchased it for ₹2,000 less and sold it for ₹1,100 less, he would have earned a 30% profit. Find the original cost price and original selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= 120% of x

= 1.20x

Under the second condition:

New cost price:

= x − ₹2,000

New selling price:

= 1.20x − ₹1,100

New profit = 30%.

Therefore:

1.20x − 1,100

= 1.30(x − 2,000)

= 1.30x − 2,600

Therefore:

1.30x − 1.20x

= 2,600 − 1,100

0.10x = 1,500

x = ₹15,000

Original selling price:

= ₹15,000 × 120%

= ₹18,000

🔍 Verification

Original profit:

= ₹18,000 − ₹15,000

= ₹3,000

Profit %:

= ₹3,000 ÷ ₹15,000 × 100

= 20%

New cost price:

= ₹15,000 − ₹2,000

= ₹13,000

New selling price:

= ₹18,000 − ₹1,100

= ₹16,900

New profit:

= ₹16,900 − ₹13,000

= ₹3,900

Profit %:

= ₹3,900 ÷ ₹13,000 × 100

= 30%

✅ Final Answer

Original Cost Price = ₹15,000

Original Selling Price = ₹18,000

---

📌 Question 84

📝 Question

A dishonest trader pays ₹500 for every kilogram purchased, but his supplier gives him 1.25 kg for every kilogram for which he pays. While selling, the trader gives only 900 g instead of 1 kg and charges ₹450 for every stated kilogram. He also spends ₹20 on transportation and handling for every actual kilogram sold. Find his actual profit percentage.

⚡ Shortcut Method

The trader pays ₹500 but receives 1.25 kg.

Therefore, actual purchase cost per kg:

= ₹500 ÷ 1.25

= ₹400

While selling, he charges ₹450 but gives only 900 g.

Actual selling price per kg:

= ₹450 ÷ 0.90

= ₹500

Additional expense:

= ₹20 per kg

Effective cost per kg:

= ₹400 + ₹20

= ₹420

Actual profit per kg:

= ₹500 − ₹420

= ₹80

Profit %:

= ₹80 ÷ ₹420 × 100

= 19.0476…%

🔍 Verification

Effective cost = ₹420 per kg

Actual selling price = ₹500 per kg

Profit = ₹80 per kg

Profit %:

= 80 ÷ 420 × 100

= 19.0476…%

✅ Final Answer

19.05% Profit approximately

---

📌 Question 85

📝 Question

A trader sells an article at a 25% profit on its cost price. From the selling price, he pays a 5% commission to an agent. He also incurs ₹500 as additional selling expenses. After paying the commission and expenses, his net profit is 12.5% of the cost price. Find the cost price and the selling price of the article.

⚡ Shortcut Method

Let cost price = ₹x

Since the trader earns 25% profit:

Selling price:

= x × 125%

= 1.25x

Commission:

= 5% of 1.25x

= 0.0625x

Net amount after commission:

= 1.25x − 0.0625x

= 1.1875x

After additional expense of ₹500:

Net amount received:

= 1.1875x − ₹500

His net profit is 12.5%.

Therefore, net amount received:

= 112.5% of x

= 1.125x

So:

1.1875x − 500 = 1.125x

0.0625x = 500

x = ₹8,000

Selling price:

= ₹8,000 × 125%

= ₹10,000

🔍 Verification

Commission:

= 5% of ₹10,000

= ₹500

Amount after commission:

= ₹10,000 − ₹500

= ₹9,500

Additional expenses:

= ₹500

Net amount:

= ₹9,500 − ₹500

= ₹9,000

Net profit:

= ₹9,000 − ₹8,000

= ₹1,000

Net profit %:

= ₹1,000 ÷ ₹8,000 × 100

= 12.5%

✅ Final Answer

Cost Price = ₹8,000

Selling Price = ₹10,000

📌 Question 86

📝 Question

A trader purchases 150 articles at ₹800 each. He sells 60 articles at a profit of 25%, 50 articles at a loss of 12%, and the remaining articles at a uniform price. After paying ₹5,000 as transportation expenses, he earns an overall profit of 15%. Find the selling price per remaining article.

⚡ Shortcut Method

Total purchase cost:

= 150 × ₹800

= ₹1,20,000

Transportation expense:

= ₹5,000

Effective total cost:

= ₹1,20,000 + ₹5,000

= ₹1,25,000

Required total selling price for 15% profit:

= ₹1,25,000 × 115%

= ₹1,43,750

First group

60 articles at 25% profit:

= 60 × ₹800 × 125%

= ₹60,000

Second group

50 articles at 12% loss:

= 50 × ₹800 × 88%

= ₹35,200

Remaining articles

= 150 − 60 − 50

= 40 articles

Required selling price:

= ₹1,43,750 − ₹60,000 − ₹35,200

= ₹48,550

Selling price per remaining article:

= ₹48,550 ÷ 40

= ₹1,213.75

🔍 Verification

Total selling price:

= ₹60,000 + ₹35,200 + ₹48,550

= ₹1,43,750

Effective cost = ₹1,25,000

Profit:

= ₹1,43,750 − ₹1,25,000

= ₹18,750

Profit %:

= ₹18,750 ÷ ₹1,25,000 × 100

= 15%

✅ Final Answer

₹1,213.75 per remaining article

---

📌 Question 87

📝 Question

A trader purchases 80 kg of a commodity at ₹750 per kg and 120 kg at ₹500 per kg. He mixes the two varieties. During processing, 5% of the mixture is lost. He sells 80 kg of the remaining mixture at ₹700 per kg and the rest at a uniform price. If he earns an overall profit of 16%, find the selling price per kg of the remaining mixture.

⚡ Shortcut Method

Cost of first variety:

= 80 × ₹750

= ₹60,000

Cost of second variety:

= 120 × ₹500

= ₹60,000

Total purchase cost:

= ₹1,20,000

Total mixture:

= 80 + 120

= 200 kg

Quantity lost:

= 5% of 200

= 10 kg

Remaining mixture:

= 200 − 10

= 190 kg

Required total selling price for 16% profit:

= ₹1,20,000 × 116%

= ₹1,39,200

Selling price of 80 kg:

= 80 × ₹700

= ₹56,000

Remaining quantity:

= 190 − 80

= 110 kg

Required selling price of remaining quantity:

= ₹1,39,200 − ₹56,000

= ₹83,200

Selling price per kg:

= ₹83,200 ÷ 110

= ₹756.3636…

🔍 Verification

First portion revenue = ₹56,000

Second portion revenue = ₹83,200

Total revenue:

= ₹1,39,200

Profit:

= ₹1,39,200 − ₹1,20,000

= ₹19,200

Profit %:

= ₹19,200 ÷ ₹1,20,000 × 100

= 16%

✅ Final Answer

₹756.36 per kg approximately

---

📌 Question 88

📝 Question

A trader sells an article at a 20% profit. If he had purchased it for ₹1,500 less and sold it for ₹900 more, his profit would have been 40%. Find the original cost price and selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= 120% of x

= 1.20x

Under the second condition:

New cost price:

= x − ₹1,500

New selling price:

= 1.20x + ₹900

Since profit is 40%:

1.20x + 900

= 1.40(x − 1,500)

= 1.40x − 2,100

Therefore:

1.40x − 1.20x

= 900 + 2,100

0.20x = 3,000

x = ₹15,000

Original selling price:

= ₹15,000 × 120%

= ₹18,000

🔍 Verification

Original profit:

= ₹18,000 − ₹15,000

= ₹3,000

Profit %:

= ₹3,000 ÷ ₹15,000 × 100

= 20%

New cost price:

= ₹15,000 − ₹1,500

= ₹13,500

New selling price:

= ₹18,000 + ₹900

= ₹18,900

New profit:

= ₹18,900 − ₹13,500

= ₹5,400

Profit %:

= ₹5,400 ÷ ₹13,500 × 100

= 40%

✅ Final Answer

Original Cost Price = ₹15,000

Original Selling Price = ₹18,000

---

📌 Question 89

📝 Question

A manufacturer sells an article to a wholesaler at a 20% profit. The wholesaler sells it to a retailer at a 25% profit. The retailer marks the article 40% above his cost price and gives a 10% discount to the customer. If the customer pays ₹9,450, find the manufacturer’s cost price.

⚡ Shortcut Method

Let manufacturer’s cost price = ₹x

Manufacturer’s selling price:

= x × 120%

= 1.20x

Wholesaler’s selling price:

= 1.20x × 125%

= 1.50x

Retailer’s marked price:

= 1.50x × 140%

= 2.10x

After 10% discount:

= 2.10x × 90%

= 1.89x

Therefore:

₹9,450 = 1.89x

x = ₹9,450 ÷ 1.89

= ₹5,000

🔍 Verification

Manufacturer sells at:

= ₹5,000 × 120%

= ₹6,000

Wholesaler sells at:

= ₹6,000 × 125%

= ₹7,500

Retailer’s marked price:

= ₹7,500 × 140%

= ₹10,500

After 10% discount:

= ₹10,500 × 90%

= ₹9,450

✅ Final Answer

₹5,000

---

📌 Question 90

📝 Question

A dishonest trader purchases 100 kg of a commodity at ₹600 per kg. His supplier gives him 1.1 kg for every kilogram for which he pays. While selling, he uses a 750 g weight instead of 1 kg and charges ₹510 for every stated kilogram. He spends ₹25 on transportation and packaging for every actual kilogram sold. Find his actual profit percentage.

⚡ Shortcut Method

The trader pays ₹600 but receives 1.1 kg.

Actual cost per kg:

= ₹600 ÷ 1.1

= ₹545.4545…

While selling, he charges ₹510 but gives only 750 g.

Actual selling price per kg:

= ₹510 ÷ 0.75

= ₹680

Additional expense:

= ₹25 per kg

Effective cost per kg:

= ₹545.4545 + ₹25

= ₹570.4545

Actual profit:

= ₹680 − ₹570.4545

= ₹109.5455

Profit %:

= ₹109.5455 ÷ ₹570.4545 × 100

= 19.201…%

🔍 Verification

Actual cost including expenses:

= ₹570.4545 per kg

Actual selling price:

= ₹680 per kg

Profit:

= ₹109.5455 per kg

Profit %:

= ₹109.5455 ÷ ₹570.4545 × 100

= 19.20% approximately

✅ Final Answer

19.20% Profit approximately

📌 Question 91

📝 Question

A trader purchases an article for ₹12,000. He marks it 50% above the cost price. He gives a discount of 20% on the marked price to one customer and an additional cashback equal to 5% of the discounted price. He also incurs ₹600 as selling expenses. Find his actual profit percentage.

⚡ Shortcut Method

Cost price:

= ₹12,000

Marked price:

= ₹12,000 × 150%

= ₹18,000

After 20% discount:

= ₹18,000 × 80%

= ₹14,400

Cashback:

= 5% of ₹14,400

= ₹720

Actual amount received:

= ₹14,400 − ₹720

= ₹13,680

Effective cost:

= ₹12,000 + ₹600

= ₹12,600

Profit:

= ₹13,680 − ₹12,600

= ₹1,080

Profit %:

= ₹1,080 ÷ ₹12,600 × 100

= 8.5714…%

🔍 Verification

Effective cost = ₹12,600

Net amount received = ₹13,680

Profit = ₹1,080

Profit percentage:

= 1,080 ÷ 12,600 × 100

= 8.5714…%

✅ Final Answer

8.57% Profit approximately

---

📌 Question 92

📝 Question

A trader buys 80 kg of a commodity at ₹480 per kg and 120 kg at ₹720 per kg. He mixes the two varieties and incurs ₹5,000 as processing expenses. During processing, 10 kg of the mixture is lost completely. He sells the remaining mixture at a uniform rate. If he earns an overall profit of 20%, find the selling price per kg of the remaining mixture.

⚡ Shortcut Method

Cost of first variety:

= 80 × ₹480

= ₹38,400

Cost of second variety:

= 120 × ₹720

= ₹86,400

Total purchase cost:

= ₹38,400 + ₹86,400

= ₹1,24,800

Processing expenses:

= ₹5,000

Total effective cost:

= ₹1,24,800 + ₹5,000

= ₹1,29,800

Required selling price for 20% profit:

= ₹1,29,800 × 120%

= ₹1,55,760

Total mixture:

= 80 + 120

= 200 kg

Quantity lost:

= 10 kg

Quantity available for sale:

= 200 − 10

= 190 kg

Selling price per kg:

= ₹1,55,760 ÷ 190

= ₹819.789…

🔍 Verification

190 × ₹819.789…

= ₹1,55,760

Profit:

= ₹1,55,760 − ₹1,29,800

= ₹25,960

Profit %:

= ₹25,960 ÷ ₹1,29,800 × 100

= 20%

✅ Final Answer

₹819.79 per kg approximately

---

📌 Question 93

📝 Question

A trader sells an article at a 25% profit. If he had purchased it for ₹2,400 more and sold it for ₹1,200 more, his profit would have been only 20%. Find the original cost price and original selling price.

⚡ Shortcut Method

Let original cost price = ₹x

Original selling price:

= 125% of x

= 1.25x

Under the second condition:

New cost price:

= x + ₹2,400

New selling price:

= 1.25x + ₹1,200

New profit = 20%.

Therefore:

1.25x + 1,200

= 1.20(x + 2,400)

= 1.20x + 2,880

Therefore:

1.25x − 1.20x

= 2,880 − 1,200

0.05x = 1,680

x = ₹33,600

Original selling price:

= ₹33,600 × 125%

= ₹42,000

🔍 Verification

Original profit:

= ₹42,000 − ₹33,600

= ₹8,400

Profit %:

= ₹8,400 ÷ ₹33,600 × 100

= 25%

New cost:

= ₹33,600 + ₹2,400

= ₹36,000

New selling price:

= ₹42,000 + ₹1,200

= ₹43,200

New profit:

= ₹43,200 − ₹36,000

= ₹7,200

Profit %:

= ₹7,200 ÷ ₹36,000 × 100

= 20%

✅ Final Answer

Original Cost Price = ₹33,600

Original Selling Price = ₹42,000

---

📌 Question 94

📝 Question

A shopkeeper purchases 240 identical articles at ₹1,250 each. He sells 80 articles at a profit of 30%. Of the remaining articles, he sells 60 articles at a loss of 20%. He then sells half of the remaining articles at a profit of 10% and the rest at a price that gives him an overall profit of 15% on the purchase cost. Find the profit percentage on the last group of articles.

⚡ Shortcut Method

Total purchase cost:

= 240 × ₹1,250

= ₹3,00,000

Required total selling price for 15% profit:

= ₹3,00,000 × 115%

= ₹3,45,000

First group

80 articles at 30% profit:

= 80 × ₹1,250 × 130%

= ₹1,30,000

Second group

60 articles at 20% loss:

= 60 × ₹1,250 × 80%

= ₹60,000

Remaining articles:

= 240 − 80 − 60

= 100 articles

Half of remaining:

= 50 articles

Third group

50 articles at 10% profit:

= 50 × ₹1,250 × 110%

= ₹68,750

Last group

Remaining articles:

= 100 − 50

= 50 articles

Required selling price from last group:

= ₹3,45,000 − ₹1,30,000 − ₹60,000 − ₹68,750

= ₹86,250

Cost of last group:

= 50 × ₹1,250

= ₹62,500

Profit:

= ₹86,250 − ₹62,500

= ₹23,750

Profit %:

= ₹23,750 ÷ ₹62,500 × 100

= 38%

🔍 Verification

Total selling price:

= ₹1,30,000 + ₹60,000 + ₹68,750 + ₹86,250

= ₹3,45,000

Total profit:

= ₹3,45,000 − ₹3,00,000

= ₹45,000

Overall profit %:

= ₹45,000 ÷ ₹3,00,000 × 100

= 15%

Last-group profit:

= ₹23,750 ÷ ₹62,500 × 100

= 38%

✅ Final Answer

38% Profit

---

📌 Question 95

📝 Question

A dealer purchases a commodity at ₹400 per kg. Due to a special arrangement with his supplier, he receives 1.125 kg for every kilogram for which he pays. While selling, he uses a 720 g weight instead of 1 kg and charges ₹432 for every stated kilogram. He also incurs ₹18 per actual kilogram sold as transportation and handling expenses. Find his actual profit percentage.

⚡ Shortcut Method

The dealer pays ₹400 but receives 1.125 kg.

Actual cost of 1 kg:

= ₹400 ÷ 1.125

= ₹355.555…

While selling, he charges ₹432 but gives only 720 g.

Actual selling price per kg:

= ₹432 ÷ 0.72

= ₹600

Additional expense:

= ₹18 per kg

Effective cost per kg:

= ₹355.555… + ₹18

= ₹373.555…

Actual profit:

= ₹600 − ₹373.555…

= ₹226.444…

Profit %:

= ₹226.444… ÷ ₹373.555… × 100

= 60.625%

🔍 Verification

Actual purchase cost per kg:

= ₹400 ÷ 1.125

= ₹355.555…

Effective cost including expenses:

= ₹373.555…

Actual selling price:

= ₹432 ÷ 0.72

= ₹600

Profit:

= ₹600 − ₹373.555…

= ₹226.444…

Profit percentage:

= ₹226.444… ÷ ₹373.555… × 100

= 60.625%

✅ Final Answer

60.625% Profit

📌 Question 96

📝 Question

A trader purchases two machines. He pays ₹40,000 for the first machine and ₹50,000 for the second machine. He sells both machines at the same selling price of ₹50,000 each. On the second machine, he spends ₹1,000 on repairs, and he pays a 2% commission on the total selling price to an agent.

Find his overall profit percentage after considering the repair and commission expenses.

⚡ Shortcut Method

Cost of first machine:

= ₹40,000

Cost of second machine:

= ₹50,000

Total purchase cost:

= ₹40,000 + ₹50,000

= ₹90,000

Total selling price:

= ₹50,000 + ₹50,000

= ₹1,00,000

Commission:

= 2% of ₹1,00,000

= ₹2,000

Repair expense:

= ₹1,000

Total effective cost:

= ₹90,000 + ₹2,000 + ₹1,000

= ₹93,000

Net amount received:

= ₹1,00,000 − ₹2,000

= ₹98,000

Profit:

= ₹98,000 − ₹93,000

= ₹5,000

Profit %:

= ₹5,000 ÷ ₹93,000 × 100

= 5.376…%

🔍 Verification

Effective cost = ₹93,000

Net selling proceeds = ₹98,000

Profit = ₹5,000

Profit percentage:

= 5,000 ÷ 93,000 × 100

= 5.38% approximately

✅ Final Answer

5.38% Profit approximately

---

📌 Question 97

📝 Question

A trader purchases an article for ₹8,800. He marks it 50% above the cost price and offers two successive discounts of 20% and 0%. After selling the article, he incurs ₹800 as transportation and handling expenses. Find his actual profit percentage.

⚡ Shortcut Method

Cost price:

= ₹8,800

Marked price:

= ₹8,800 × 150%

= ₹13,200

Discount:

= 20%

Selling price:

= ₹13,200 × 80%

= ₹10,560

Additional expenses:

= ₹800

Effective cost:

= ₹8,800 + ₹800

= ₹9,600

Profit:

= ₹10,560 − ₹9,600

= ₹960

Profit %:

= ₹960 ÷ ₹9,600 × 100

= 10%

🔍 Verification

Effective cost = ₹9,600

Selling price = ₹10,560

Profit = ₹960

₹960 is exactly 10% of ₹9,600.

✅ Final Answer

10% Profit

---

📌 Question 98

📝 Question

A trader purchases 15 identical articles for the price he would normally pay for 12 articles. The normal cost price of each article is ₹1,200. He sells 8 articles at a profit of 25% and the remaining 7 articles at a loss of 10%.

Find his overall profit percentage.

⚡ Shortcut Method

Normal cost of one article:

= ₹1,200

Normal cost of 12 articles:

= 12 × ₹1,200

= ₹14,400

Therefore, actual purchase cost of 15 articles:

= ₹14,400

First group

8 articles sold at 25% profit:

= 8 × ₹1,200 × 125%

= ₹12,000

Second group

7 articles sold at 10% loss:

= 7 × ₹1,200 × 90%

= ₹7,560

Total selling price:

= ₹12,000 + ₹7,560

= ₹19,560

Profit:

= ₹19,560 − ₹14,400

= ₹5,160

Profit %:

= ₹5,160 ÷ ₹14,400 × 100

= 35.833…%

🔍 Verification

Actual cost = ₹14,400

Total selling price = ₹19,560

Profit = ₹5,160

Profit percentage:

= 5,160 ÷ 14,400 × 100

= 35.83% approximately

✅ Final Answer

35.83% Profit approximately

---

📌 Question 99

📝 Question

A trader purchases 100 kg of a commodity at ₹1,000 per kg. He sells 60% of the quantity at a profit of 20%, one-fourth of the remaining quantity at a loss of 10%, and the rest at a 15% profit. He also incurs ₹2,000 as transportation and storage expenses.

Find his overall profit percentage.

⚡ Shortcut Method

Total purchase cost:

= 100 × ₹1,000

= ₹1,00,000

Additional expenses:

= ₹2,000

Effective total cost:

= ₹1,00,000 + ₹2,000

= ₹1,02,000

First group

60% of 100 kg:

= 60 kg

Selling price at 20% profit:

= 60 × ₹1,000 × 120%

= ₹72,000

Second group

Remaining quantity:

= 100 − 60

= 40 kg

One-fourth of 40 kg:

= 10 kg

Selling price at 10% loss:

= 10 × ₹1,000 × 90%

= ₹9,000

Third group

Remaining quantity:

= 40 − 10

= 30 kg

Selling price at 15% profit:

= 30 × ₹1,000 × 115%

= ₹34,500

Total selling price:

= ₹72,000 + ₹9,000 + ₹34,500

= ₹1,15,500

Profit:

= ₹1,15,500 − ₹1,02,000

= ₹13,500

Profit %:

= ₹13,500 ÷ ₹1,02,000 × 100

= 13.235…%

🔍 Verification

Effective cost = ₹1,02,000

Total selling price = ₹1,15,500

Profit = ₹13,500

Profit percentage:

= 13,500 ÷ 1,02,000 × 100

= 13.24% approximately

✅ Final Answer

13.24% Profit approximately

---

📌 Question 100

📝 Question

A trader purchases 25 calculators at a marked price of ₹2,000 each. The manufacturer gives him a 18% trade discount, followed by an additional 5% cash discount on the reduced price.

The trader then sells 20 calculators at a profit of 25% and the remaining 5 calculators at a loss of 10%.

Find his overall profit percentage.

⚡ Shortcut Method

Marked price per calculator:

= ₹2,000

After 18% trade discount:

= ₹2,000 × 82%

= ₹1,640

After 5% cash discount:

= ₹1,640 × 95%

= ₹1,558

Actual cost of one calculator:

= ₹1,558

Total cost of 25 calculators:

= 25 × ₹1,558

= ₹38,950

First group

20 calculators sold at 25% profit:

= 20 × ₹1,558 × 125%

= ₹38,950

Second group

5 calculators sold at 10% loss:

= 5 × ₹1,558 × 90%

= ₹7,011

Total selling price:

= ₹38,950 + ₹7,011

= ₹45,961

Profit:

= ₹45,961 − ₹38,950

= ₹7,011

Profit %:

= ₹7,011 ÷ ₹38,950 × 100

= 18%

🔍 Verification

Total cost = ₹38,950

Total selling price = ₹45,961

Profit = ₹7,011

Profit percentage:

= 7,011 ÷ 38,950 × 100

= 18% exactly

✅ Final Answer

18% Profit

❓ FAQ Section

What are Profit and Loss questions?

Profit and Loss questions test your ability to calculate profit, loss, selling price, cost price, marked price, discount, and percentage changes. They are frequently asked in banking, SSC, railway, and insurance exams.

Are these 100 Profit and Loss questions suitable for banking exams?

Yes. The questions are designed for IBPS PO, SBI PO, RBI Assistant, LIC AAO, SSC CGL, RRB, and similar competitive examinations.

Are detailed solutions included?

Yes. Every question comes with a step-by-step solution, shortcut method, and exam tip.

What is the difficulty level?

The questions range from basic to moderate and help build a strong foundation for competitive exams.

Can beginners solve these questions?

Yes. The questions are arranged progressively, making them suitable for beginners as well as experienced aspirants.

Related Profit and Loss Practice Sets

• Profit and Loss Questions (1–10)
• Profit and Loss Questions (11–20)
• Profit and Loss Questions (21–30)
• Profit and Loss Questions (31–40)

⚡ 10 Profit and Loss Shortcut Tricks

Master these simple tricks to solve Profit and Loss questions faster in banking and competitive exams.

1. Assume Cost Price = ₹100

If only percentages are given, assume the Cost Price (CP) is ₹100. This makes calculations much easier.

Profit % = (Profit ÷ Cost Price) × 100

2. Remember the Profit Formula

Always calculate profit based on the Cost Price, not the Selling Price.

3. Remember the Loss Formula

Loss % = (Loss ÷ Cost Price) × 100

Loss percentage is also calculated on the Cost Price.

4. Successive Discount Trick

Net Discount = A + B − (A × B ÷ 100)

Example:

20% and 10%

Net Discount = 20 + 10 − 2 = 28%

5. Reverse Cost Price Formula

If Profit % is given:

Cost Price = (Selling Price × 100) ÷ (100 + Profit%)

If Loss % is given:

Cost Price = (Selling Price × 100) ÷ (100 − Loss%)

6. Effective Cost Price

Always include expenses like transportation, labour, packaging, repair, loading, and insurance in the Cost Price.

Effective Cost Price = Purchase Cost + Additional Expenses

7. Markup and Discount Trick

Instead of calculating Marked Price and Selling Price separately, multiply the percentage factors directly.

Example:

125% × 80% = 100%

Therefore, No Profit, No Loss.

8. Damaged Goods Rule

Even if some goods are damaged, their purchase cost remains part of the total Cost Price. Only the Selling Price changes.

9. Learn Common Percentage Values

• 50% = 1/2
• 25% = 1/4
• 20% = 1/5
• 12.5% = 1/8
• 10% = 1/10
• 5% = 1/20

These conversions save valuable time in exams.

10. Solve Without a Calculator

Practice multiplying and dividing numbers mentally. Banking exams are speed-based, and strong mental calculations can significantly improve your performance.

🚀 Continue Your Quantitative Aptitude Preparation

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🎯 Final Challenge Question

Let’s test your understanding!

A shopkeeper purchased an article for ₹2,500. He marked it 40% above the cost price and then offered a 15% discount on the marked price.

What is the profit percentage?

A. 15%

B. 18%

C. 19%

D. 20%

Write your answer in the comments section along with your solution. We’d love to see your approach!